Probability Questions and Answers

3 Marbles You have a bag of 15 marbles 6 blue 4 red 3 yellow 2 green You draw out two marbles without replacement from the bag If you draw two red marbles you win 61 tickets If you draw at least one yellow marble you win 6 tickets If you draw two blue marbles you lose 40 tickets the cost to play Otherwise you break even

A population of values has a normal distribution with 18 4 and a 41 4 a Find the probability that a single randomly selected value is less than 19 Round your answer to four decimal places P X 19 b Find the probability that a randomly selected sample of size n 197 has a mean less than 19 Round your answer to four decimal places P M 19

V V IV 1 10 2 hen purchasing bulk orders of batteries a toy ipment is accepted if at most 3 batteries do no cepted Will almost all such shipments be acc e probability that this whole shipment will be ound to four decimal places as needed he company will accept of the shipments ound to two decimal places as needed

5 3 10 1 10 2 Students Given Four Quarters Students Given a 1 Bill Question 16 o an experiment college students were given either four quarters or a 1 bill and they elow Purchased Gum Kept the Money 34 13 18 31

Each of two parents has the genotype blond brown which con least one blond allele that color will dominate and the child s h a List the different possible outcomes Assume that these out

How many 6 letter passords can be made using the letters A thought Z if a Repetition of letters is allowed b Repetition of letters is not allowed

A 4 digit PIN number is selected What it the probability that there are no repeated digits The probability that no numbers are repeated is Write your answer in decimal form rounded to the nearest thousandth Question Help Vid

In Alex s drawer she has 11 pairs of socks 8 of which are white and 10 tee shirts 6 of which are white The probability of choosing a white pair of socks is The probability of choosing a white tee shirt is The probability of both being white is Write your answers of reduced fractions

You randomly select one card from a 52 card deck Find the probability of selecting a three or a four The probability is Type an integer or a fraction Simplify your answer

In a certain state s lottery 45 balls numbered 1 through 45 are placed in a machine and six of them are drawn at random If the six numbers drawn match the numbers that a player had chosen the player wins 1 000 000 In this lottery the order in which the numbers are drawn does not matter Compute the probability that you win the million dollar prize if you purchase a single lottery ticket Write your answer as a reduced fraction P win A single lottery ticket costs 2 Compute the Expected Value to the state if 10 000 lottery tickets are sold Round your answer to the nearest dollar Answer A single lottery ticket costs 2 Compute the Expected Value to you if you purchase 10 000 lottery tickets Round your answer to the nearest dollar

A poker hand consists of five cards randomly dealt from a standard deck of 52 cards The order of the cards does not matter Determine the following probabilities for a 5 card poker hand Write your answers in percent form rounded to 4 decimal places Determine the probability that exactly 4 of these cards are Aces Answer Determine the probability that all five of these cards are Spades Answer Determine the probability that exactly 4 of these cards are face cards Answer 11 Determine the probability of selecting exactly 2 Aces and exactly 2 Kings Answer Determine the probability of selecting exactly 1 Jack

There are twelve female board members and eighteen male board members How many ways are there to make a committee of ten board members ways How many ways are there to make a committee of ten board members if exactly three must be female Answer ways Determine the probability of selecting a committee of ten board members where exactly three of the members were female Write your answer as a decimal rounded to the nearest thousandth

4 letters are typed with repetition allowed What is the probability that all 4 will be vowels Write your answer as a percent Round to the nearest hundredth of a percent as needed The probability is

What is the probability that if 4 letters are typed no letters are repeated Write your answer in decimal form rounded to the nearest thousandth The probability that no letters are repeated is Hel FYI

5 letter words are formed using the letters A B C D E F G How many such words are possible for each of the following conditions a No condition is imposed There are b No letter can be repeated in a word There are There are c Each word must begin with the letter A d The letter C must be at the end There are possible words possible words There are possible words possible words e The second letter must be a vowel possible words

3 letters are typed without repetition What is the probability that all 3 will be vowels Write your answer as a percent Round your answer to three decimal places The probability is

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories Smooth Rhythm or Standard The results were then presented to the owner i the following Venn Diagram Smooth 8 10 7 15 Standard 14 Rhythm 13 5 Determine the following probabilities Write your answers in percent form rounded to the nearest tenth W a P Smooth b P Rhythm and Standard c P Smooth or Standard B d P Rhythm or Smooth

How many three letter words can be made from 4 letters FGHI if repetition of letters a is allowed There are b is not allowed There are possible three letter words possible three letter words

A gate has a standard key pad with the digits 0 through 9 How many possible code combinations are there if the code is 6 digits long There are different code combinations

Given the following information P A 0 65 P B 0 6 P A and B 0 51 P B given A 0 4 What is the probability of A or B Round your answer to the nearest hundredth as neec P A or B Question Help Video Message instructor

Compute the probability of drawing two clubs from a standard deck of 52 cards Round your answer to four decimal places Answer Compute the probability of drawing two face cards from a standard deck of 52 cards Round your answer to four decimal places Answer Compute the probability of drawing two aces from a standard deck of 52 cards Round your answer to four decimal places

A math class consists of 14 female students and 17 male students Two students are selected at random to participate in a probability experiment Compute the following probabilities Write your answers in decimal form Round to the nearest thousandth as needed a A male is selected then a female b A female is selected then a male c Two males are selected d Two females are selected e No males are selected

Istas buys a bag of cookies that contains 8 chocolate chip cookies 7 peanut butter cookies 5 sugar cookies and 4 oatmeal cookies What is the probability that Istas reaches in the bag and randomly selects a chocolate chip cookie from the bag eats it then reaches back in the bag and randomly selects a sugar cookie Write your answer as a percent Round to the nearest tenth of a percent Answer Question Help Video Message instructor

Below is a list of all possible outcomes in the experiment of rolling two die 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 4 1 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 2 4 3 4 4 4 5 4 6 5 2 5 3 5 4 5 5 5 6 5 1 6 1 6 2 6 3 6 4 6 5 6 6 Determine the following probabilities Write your answers as reduced fractions P sum is odd P sum is 5 P sum is 7 P sum is 7 and one of the die is a 1

Smooth 14 7 8 Standard 5 Rhythm 4 10 11 Use the Venn Diagram to determine the following probabilities Write your answers in percent form rounded to the nearest tenth If a student is chosen at random what is the probability that the student competed in Rhythm GIVEN they had competed in Smooth P Rhythm Smooth If a student is chosen at random what is the probability that the student competed in Rhythm GIVEN they had competed in Standard P Rhythm Standard If a student is chosen at random what is the probability that the student competed in Standard GIVEN they had competed in Rhythm P Standard Rhythm If a student is chosen at random what is the probability that the student competed in Rhythm GIVEN they had competed in Smooth or Standard P Rhythm Smooth or Standard

Suppose a jar contains 7 red marbles and 20 blue marbles If you reach in the jar and pull out 2 marbles at random find the probability that both are red Write your answer as a reduced fraction Answer

A home pregnancy test was given to women then pregnancy was verified through blood tests The following table shows the home pregnancy test results Positive Negative Pregnant Not Pregnant Total Round your answers to the nearest thousandth P positive pregnant P pregnant positive P negative pregnant 52 6 58 P not pregnant negative Total 56 65 121 4 59 63

Jenelle draws one from a standard deck of 52 cards Determine the probability of drawing either a king or a ten Write your answer as a reduced fraction Answer Determine the probability of drawing either a king or a club Write your answer as a reduced fraction Answer

A die is rolled twice What is the probability of showing a 3 on the first roll and an even number on the secon roll Write your answer as a simplified fraction Answer

Amber rolls a 6 sided die On her first roll she gets a 1 She rolls again a What is the probability that the second roll is also a 1 P 1 1 b What is the probability that the second roll is a 2 B

The table summarizes results from 982 pedestrian deaths that were caused by automobile accidents Driver Intoxicated Yes No Pedestrian Intoxicated Yes No 44 84 245 609 If one of the pedestrian deaths is randomly selected find the probability that the pedestrian was not intoxicated or the driver was intoxicated Report the answer as a percent rounded to one decimal place accuracy You need not enter the symbol prob Question Help Video 1 Video

Joann s is having a sale on fabric and you are rummaging through the sale bin In it there are 9 cream fabrics 6 blue fabrics 11 pink fabrics and 5 green fabrics You randomly pull fabrics from the bin without replacement Use three decimal places in your answers a Find the probability of drawing a blue fabric then a cream then a pink and then another pink fabric b Find the probability of drawing a green fabric and then NOT a green fabric c For parts a and b state what fractions you used and what you did with them Basically explain how you got your answers

Suppose that 24 of people own dogs Suppose you sample three people at random Use three decim places in your answers to the following questions a What is the probability that all three of them own dogs b What is the probability that none of the three of them own dogs c What is the probability that at least one of them own a dog

A group of students took a test Below are the summary of grades and where the students sat in the classroom Find the probabilities below and write the answer as a fraction Passed Did Not Pass Total Back of Classroom 10 12 22 Middle of Classroom 5 12 17 Front of Classroom 12 15 27 Total 27 39 66 a If one student is chosen at random find the probability that the student did not pass the test b If one student is chosen at random find the probability that the student passed the test OR sat in the middle of the classroom

In 5 card poker played with a standard 52 card deck 52 C5 or 2 598 960 different hands are possible The probability of being dealt various hands is the number of different ways they can occur divided by 2 598 960 Shown to the right is the number of ways a particular type of hand can occur and its associated probability Find the probability of not being dealt this type of hand Number of Ways the Hand Can Occur 696 Probability 696 2 598 960

In 5 card poker played with a standard 52 card deck 52C5 or 2 598 960 different hands are possible The probability of being dealt various hands is the number of different ways they can occur divided by 2 598 960 Shown to the right is the number of ways a particular type of hand can occur and its associated probability Find the probability of not being dealt this type of hand Number of Ways the Hand Can Occur 9764 Probability 9764 2 598 960

None of the above n 3 of 10 hary fair die is a cube with the numb rolled twice in succession and that th e of a single trial of a random experin te the probability of each of the follow

sentence or two explaining your reasoning or calculations you did in R 1 A certain electric car company claims publicly that their car batteries will last for at least 300 000 miles An internal study done by the company showed that the lifespans of their car batteries followed a normal probability distribution with a mean lifespan of 400 000 miles and a standard deviation of 60 000 miles What percent of their car batteries will fail to meet the public claim of lasting at least 300 000 miles Round to the nearest tenth of a percent a 2 4 b 4 8 c 5 6 36000 M 400 60000 P 22 167 P 2 1 67 by 2 table G0 95254 20 96 96 d 8 4 D 2 mean M 400 000 S d 6 60 000 P x 300 9 6 300 P Z 100 000 2000 3

Weights of newborn babies in a certain state have normal distribution with mean 7 3 and standard deviation 1 2 lb A random sample of 64 newborns is selected Let x represent the mean weight of the sample What is the probability that the sample mean weight x is more than 7 5 lb

Sara draws the 2 of hearts from a standard deck of 52 cards Without replacing the first card she then proceeds to draw a second card a Determine the probability that the second card is another 2 P 2 2 of hearts b Determine the probability that the second card is another heart P heart 2 of hearts c Determine the probability that the second card is a club P club 2 of hearts d Determine the probability that the second card is a 5 P 5 2 of hearts

A 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

If the odds for a certain event are 23 to 18 what is the probability of the event occuring Write your answer as a simplified fraction

A ball is drawn randomly from a jar that contains 4 red balls 2 white balls and 6 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

If you randomly select a card from a well shuffled standard deck of 52 cards determine the probability that the card you select is a spade 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 de

If you randomly select a letter from the phrase I like to swim at the Recreation Pavilion what is the probability that you select a vowel Your answer must be in the form of a reduced fraction P vowel

Find the odds for rolling a 6 sided die and getting a 2 to Find the odds against rolling a 6 sided die and getting a 2 to Simplify your answers

The manager of the dairy section of a large supermarket chose a random sample of 200 egg cartons and found that 90 cartons had at least one broken egg Let p denote the proportion of all cartons which have at least one broken egg Find a point estimate for p and also construct a 90 confidence interval for p

Suppose 170 randomly selected people are surveyed to determine if they own a tablet Of the 170 surveyed 69 reported owning a tablet Using a 95 confidence level compute a confidence interval estimate for the true proportion of people who own tablets Give your answer to four decimal places if necessary

In her MAT135 class professor Alayeb found that the mean score of the first exam was 74 Suppose that the scores are normally distributed with a standard deviation of 15 points What is the probability that a randomly selected score is less than 70 P x 70 What is the probability that a randomly selected score is more than 89 P x 89 what is the probability that a randomly selected score is between 70 and 89 P 70 x 89

A distribution of values is normal with a mean of 168 4 and a standard deviation of 16 Find P1 which is the score separating the bottom 81 from the top 19 Ps1 Enter your answer as a number accurate to 1 decimal place Answers obtained using exact z scores or z scores rounded to 3 decimal places are accepted