# Probability Questions and Answers

Statistics

ProbabilityCar inspection: Of all the registered automobiles in a city, 11% fail the emissions test. Fourteen automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places.
(a) Find the probability that exactly five of them fail the test.
The probability that exactly five of them fail the test is
(b) Find the probability that fewer than five of them fail the test.
The probability that fewer than five of them fail the test is
(c) Find the probability that more than four of them fail the test.
The probability that more than four of them fail the test is

Statistics

ProbabilityTake a guess: A student takes a multiple-choice test that has 11 questions. Each question has four choices. The student guesses
randomly at each answer. Let X be the number of questions answered correctly. Round the answers to at least four decimal
places.
Part: 0/2
Part 1 of 2
(a) P (4)

Statistics

ProbabilityAn airliner carries 400 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of
2.8 in. Complete parts (a) through (d).
a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability is.
(Round to four decimal places as needed.)

Statistics

ProbabilityThe value given below is discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.
Probability of more than 3 passengers who do not show up for a flight
Choose the correct answer below.
A. The area to the right of 2.5
B. The area between 2.5 and 3.5
C. The area to the left of 2.5
D. The area to the left of 3.5
E. The area to the right of 3.5

Statistics

ProbabilityHigh blood pressure: A national survey reported that 31% of adults in a certain country have hypertension (high blood pressure). A sample of 21 adults is studied. Round the answer to at least four decimal places.
(a) What is the probability that exactly 5 of them have hypertension?
The probability that exactly 5 of them have hypertension is
(b) What is the probability that more than 7 have hypertension?
The probability that more than 7 have hypertension is

Statistics

ProbabilityIf np ≥ 5 and nq 25, estimate P(at least 11) with n = 13 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq<5, then state that the normal approximation is not suitable.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. P(at least 11)=
(Round to three decimal places as needed.)
B. The normal distribution cannot be used.

Statistics

ProbabilityIn a survey of 1084 people, 725 people said they voted in a recent presidential election. Voting records show that 64% of eligible voters actually did vote. Given that
64% of eligible voters actually did vote, (a) find the probability that among 1084 randomly selected voters, at least 725 actually did vote. (b) What do the results from part (a) suggest?
(a) P(X≥ 725)= (Round to four decimal places as needed.)
w

Statistics

ProbabilityA probability experiment consists of rolling a 6-sided die. Find the probability of the event below. rolling a number less than 5
The probability is (Type an integer or decimal rounded to three decimal places as needed.)

Statistics

ProbabilityUse the chip model to find (-2) x 4. Show process. Your model needs to show (-2) x 4 rather than showing an
equivalent expression such as - 2 x 4.
Please use
to represent -1 and use O to represent +1.

Statistics

ProbabilityQuestion 10 (1 point)
Sherlock and Mycroft each have a complete deck of cards. Each man picks one card
at random from his deck. Each man has probabilities corresponding to his deck. The
two cards chosen are "independent" of each other, which means that both-events-
together have probabilities that multiply.
If Sherlock and Mycroft each pick one card at random from their decks, what is the
probability that both Sherlock gets a heart and Mycroft gets a heart?

Statistics

ProbabilityJohn has a bucket with 300 glass marbles in it. 100 of the marbles have 'spots,' the rest of the marbles are one of the solid colors blue or green or black or white.
If John draws one marble at random out of his bucket, what is the probability he DOES NOT gets a 'spots' marble?

Statistics

ProbabilityDraw one card at random from a well-shuffled deck.
What is the probability that the card chosen is a 'spade, just not the ace of spades?
Count outcomes carefully.

Statistics

ProbabilityIn a certain large city, 23% of cars are purple. If you pick a car in this city at random, what is the probability that you do NOT get a purple car?

Statistics

ProbabilityWhen you have equal probabilities, the probability of a Happy Event is
ways-to-be-Happy/total-possibilities.
John has a bucket with 300 glass marbles in it. 100 of the marbles have 'spots,' the
rest of the marbles are one of the solid colors blue or green or black or white.
If John draws one marble at random out of his bucket, each of the individual marbles
is equally likely to be chosen. What is the probability he gets a 'spots' marble?

Statistics

ProbabilitySherlock has a well-shuffled complete deck of cards. John has a bucket with 300
glass marbles in it. 100 of the marbles have 'spots, the rest of the marbles are one of
the solid colors blue or green or black or white.
If Sherlock picks one card at random from his deck and John picks one marble at
random from his bucket, the two events are independent of each other, and
probabilities multiply.
What is the probability that Sherlock gets a card and John gets a marble?

Statistics

ProbabilityThe cholesterol levels of 14-year-old boys are Normally distributed with mean 17 mg/dL and standard deviation 30 mg/dL.
Suppose you pick a 14-year-old boy at random and measure his cholesterol.
What is the probability that his cholesterol is less than 140?

Statistics

Probabilitypoint)
In a certain large city, 23% of cars are purple. This is a very large city. If we pick one
car at random and set it aside, the rest of the cars are still 23% purple. Even if we
pick two or three cars and set them aside, the rest of the cars are still 23% purple.
If we choose three cars at random, the cars are 'independent' of each other.
Probability for all three cars is therefore probability for each car, multiplied together.
What is the probability that all three randomly chosen cars are purple?

Statistics

ProbabilityIf I roll one 4-sided die and one 10-sided die, what is the chance that the total number of spots is 10?

Statistics

ProbabilityA pet store has 9 puppies, including 3 poodles, 4 terriers, and 2 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)

Statistics

ProbabilityA bag contains 36 red blocks, 48 green blocks, 22 yellow blocks, and 19 purple blocks. You pick one block from the bag at random. Find the theoretical probability. Write your answer as a fraction in simplest form in the form a/b.
P(purple or not red)

Statistics

ProbabilityTwo fair number cubes are rolled. Determine whether the events are mutually exclusive.
The sum is a prime number; the sum is less than 4.
The sum is odd; the numbers are equal.
Both numbers are odd; the sum is even.
Both numbers are odd; the sum is even.
The product is greater than 20; the product is a multiple of 3.

Statistics

ProbabilityA standard number cube is tossed. Find the following probability.
P(less than 3 or odd)

Statistics

ProbabilityWhich of the following are mutually exclusive events when a single card is chosen at random from a standard deck of 52 playing cards? Choose all that apply.
a. Choosing a 6 and choosing a club.
b. Choosing a 7 and choosing a jack.
c. Choosing a 10 and choosing a heart.
d. Choosing an ace and choosing an 8.

Statistics

ProbabilityMike and Ava decided to see who is better at the online game "Squashing Sweets. They each played three games. Mike's scores were 85, 122, and 117. Ava's scores
were 107, 116, and 101.
Who is the better player -Mike or Ava? Also, what information gives you confidence in your conclusion?
Elimination Tool
Select one answer
A Ava is the better player since her scores are consistently above 100 points.
B Mike is the better player since his median score is higher than Ava's highest score.
C Mike is the better player. Although he had one bad game, two of his three scores were higher than two of Ava's three scores.
D Mike and Ava are equally good at the game, since the average for both of their scores is the same.
E There is not enough information to determine who is the better player, because the results from these three games may be simply due to chance.

Statistics

ProbabilityA card is drawn randomly from a standard 52-card deck. Find the following:
Write all answers as simplified fractions (not mixed numbers).
Probability the card drawn is a face card
Probability the card drawn is not a face card.
Odds in favor of drawing a face card
Odds against drawing a face card

Statistics

ProbabilityA ball is drawn randomly from a jar that contains 7 red balls, 6 white balls, and 3 yellow balls. Find the
probability of the given event. Write your answers as reduced fractions or whole numbers.
(a) P(A red ball is drawn) =
(b) P(The ball drawn is NOT red) =
(c) P(A green ball is drawn) =

Statistics

ProbabilityIf you randomly select a card from a well-shuffled standard deck of 52 cards, determine the probability that the card you select is a 6.
a) Write your answer as a reduced fraction.
b) Write your answer as a decimal, rounded to the nearest thousandth.
c) Write your answer as a percent. Round to the nearest tenth of a percent as needed.

Statistics

ProbabilityAssume that adults have IQ scores that are normally distributed with a mean of μ = 105 and a standard deviation o=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.
The probability that a randomly selected adult has an IQ between 93 and 117 is
(Type an integer or decimal rounded to four decimal places as needed.)

Statistics

ProbabilityThe waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
(Simplify your answer. Round to three decimal places as needed.)

Statistics

ProbabilityYou want to rent an unfurnished one-bedroom apartment in Durham, NC next year. The mean monthly rent for a random sample of 60 apartments advertised on Craig's List (a website that lists apartments for rent) is $1000. Assume a population standard deviation of $200. Construct a 95% confidence interval.
CL = 0.95, a = 0.05

Statistics

ProbabilityHal and Renee play the following game. A bag has 14 tiles in it, each with a letter from the two word phrase the probability on it. Hal and Renee take turns drawing a tile, recording the letter, and placing the tile back in the bag. Renee earns a point if she draws a vowel. Hal earns a point if he draws a consonant. They decide that the letter y can be a vowel or a consonant.
Is the following statement True or False.
The game is fair because Hal and Renee have the same probability of drawing a winning letter.
Select one:
True
False

Statistics

ProbabilityUSE THE INFORMATION BELOW TO ANSWER QUESTIONS 22 THRU 23
In recent years home lighting technology has changed dramatically due to the development of Light
Emitting Diode (LED) bulbs. Although previously used mainly in traffic lights and although LED
bulbs are more expensive than incandescent bulbs, they use approximately 90% less energy and
they last up to 25 times longer than incandescent bulbs. It has been estimated that the average
home saves $250 per year using LED bulbs rather than incandescent bulbs. One popular
manufacturer of LED bulbs claim that nearly all of their 75-watt LEDs will last for more than 25,000
hours.
Question 22
Suppose that a small company purchases 300 of these 75-watt LEDs with a guarantee that 97% of
them will last for more than 25,000 hours. Assuming the guarantee is correct, what is the
probability that at least 280 of them will last for more than 25,000 hours?
0.9669
0.9845
0.9741
1 pts
0.9997

Statistics

ProbabilityBy rewriting the formula for the multiplication rule, you can write a formula for finding
conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A) = -
information below to find the probability that a flight departed on time given that it arrives on time.
P(A and B)
P(A)
The probability that an airplane flight departs on time is 0.89.
The probability that a flight arrives on time is 0.89.
The probability that a flight departs and arrives on time is 0.82.
Use the

Statistics

ProbabilityIn a survey of U.S. adults with a sample size of 2003, 358 said Franklin Roosevelt was the best president since World War II. Two U.S.
adults are selected at random from this sample without replacement. Complete parts (a) through (d).
(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.
The probability that both adults say Franklin Roosevelt was the best president since World War II is 0.032.
(Round to three decimal places as needed.)
(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.
The probability that neither adult says Franklin Roosevelt was the best president since World War II is
(Round to three decimal places as needed.)

Statistics

ProbabilityA process yields 14% of defective items. If 100 items are randomly selected from the process, find the following probabilities
(a) The probability that the number of defectives exceeds 15
(b) The probability that the number of defectives is less than 12

Statistics

ProbabilityA coin is tossed 484 times. Use the normal curve approximation to find the probability of obtaining
(a) between 226 and 254 heads inclusive;
(b) exactly 245 heads;
(c) fewer than 216 or more than 269 heads.

Statistics

ProbabilityA pair of dice is rolled 120 times. What is the probability that a total of 7 occurs
(a) at least 16 times?
(b) between 24 and 30 times inclusive?
(c) exactly 20 times?

Statistics

ProbabilityStatistics released by a reputable traffic safety organization show that on an average weekend night, 1 out of every 10 drivers on the road is drunk. If 300 drivers are randomly checked next Saturday night, what is the probability that the number of drunk drivers will be
(a) less than 24?
(b) more than 332
(c) at least 36 but less than 40?

Statistics

ProbabilityA pair of dice is rolled 240 times. What is the probability that a total of 7 occurs
(a) at least 28 times?
(b) between 41 and 49 times inclusive?
(c) exactly 40 times?

Statistics

ProbabilityResearchers at a reputable university and a reputable health organization claim that approximately 76% of people believe "tranquilizers work very well to make a person more calm and relaxed" Of the next 75 people interviewed, what is the probability that
(a) at least 45 are of this opinion?
(b) at most 49 are of this opinion?
(a) The probability is
(Round to four decimal places as needed.).

Statistics

ProbabilityIf we pick one Spring 2011 Math 1530 student at random, what is the probability
that we get a male student?
PERCENT ANSWER WITH TWO PLACES AFTER THE DECIMAL.

Statistics

ProbabilityA bag contains 6 orange marbles and 7 green marbles. A marble is selected from the bag at random, set aside, and then another marble is selected. Which of the following choices shows the correct calculation of the probability that both marbles are orange?
select one
O 7/13 6/12 = 7/26
O 6/13 . 6/13 = 36/169
O 6/13 . 5/13 = 30/169
O 6/13 . 5/12 = 5/26

Statistics

ProbabilityA clothing store has 18 suits for sale. 10 of the suits are blue, and 8 are black. Two suits are chosen to be put on display on the store window. What is the probability that both suits will be black?
Select one:
O 9/144
O 7/306
O 28/153
O 4/9

Statistics

ProbabilityNadir and Grady work at a company with 50 employees total. The company is going to promote two employees to a director and a manager role. What is the probability that both positions are given to Nadir and Grady?
Select one:
O 1/2450
O 1/1225
O 1/100
O 1/2500

Statistics

ProbabilityA single card is drawn at random from a standard deck of cards. What is the probability of drawing
a queen or a diamond?
Select one:
O 1/4
O 4/13
O 1/52
O 17/52

Statistics

Probability10 candidates are running for president and vice president positions. What is the probability that a
particular candidate does not win a position?
Select one
1/5
4/5
1/20
1/10