Question

BIU A IE E E - ** 11 na A, Search the menus (Alt+) 100 % Normal text Calibri 1 2 3 4 Show your calculation and give your answer in the fraction form and in the decimal form to receive full credit. 1. Let's play "Craps" 5 points A favorite casino game of dice "craps is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called "craps") the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (in which case the player wins) until a 7 occurs (in which case the player loses). When answering the following questions, you can use this outcome chart for the roll of two dice: . What is the probability that a player wins the game on the first roll of dice? b. What is the probability that a player loses the game on the first roll of dice? If the player throws a total of 4 on the first roll, what is the probability that the player wins the next roll? C. the next roll? d. If the player throws a total of 4 on the first roll, what is the probability that the player loses If the player throws a total of 4 on the first roll, what is the probability that the game ends in the next roll? e. (win or lose) B IUA na A, Search the menus (Alt+/) 100% Normal text Calibri 11 1 2 3 4 5 6 7 Car Inventory-6 points 1 A car dealer sold 750 automobiles last year. The following table categorizes the cars sold by size and color and ndom from the 750 for which the e s the number of cars in each will win a lifetime of free oil changes. Give your answer as a fraction and as a decimal (up to 4 decimal places) in the given spaces. Total White Black Red Grey Small 134 102 33 Midsize 86 63 36 105 Large 26 32 22 40 Total What is the probability that the car is white AND large? b. What is the probability that the ca is red OR small? the probability that it is midsize? Given that the car white, what d. Given that the car is large, what is the probability that it is red? Given that the car is red, what is the probability that it is large? e Determine whether color and size are independent. Justify your answer by showing your work here. (HINT: Use multiplication rule or conditional probabilities from above) 11 BIUA Search the menus (Alt+) na A 100 % - Normal text Calibri CD 1 2 3 4 5 6 7 Are they really different? - points 1. With so many men's and women's versions of different products, you might wonder how different they really are. To help answer this question, technicians at Consumers Advocate compared a new antiperspirant for women (A) with a leading antiperspirant for women (B) and a leading antiperspirant for men (C). A randomly selected group of 30 women consumers was asked to use each product over a 3-week period, (one product for one week) following a random design. At the end of each week, the women were asked rate the antiperspirants on a 5-point scale, with 1 being Poor and 5 being Excellent. The following table contains a summary of the results for this question. Survey Results for Antiperspirant Study Rating Antiperspirant Fair to Good Very Good to Excellent Poor 1. 8 21 A 0 11 19 C 11 13 Using the information in the table answer the following questions. Provide your answers in the fraction form and in ecimal form. What is the probability that a randomly selected antiperspirant scored Very Good to Excellent? a. b. What is the probability that a randomly selected antiperspirant is type B? What is the probability randomly selecting antiperspirant B, given that the score was Fair to Good. d. What is the probability f receiving a Very Good to Excellent rating, given that antipersspirant C was selected? Determine whether the antiperspirant type and rating are independent. Use your results from above to e. justify your answer.

Answer 1

a.
Probability that the player wins on the first roll = Probability that the player throws 7 or 11

We can get 7 as (1,6), (2, 5), (3, 4), (4, 3) , (5, 2) , (6, 1) out of 36 combinations.

So, probability to throw 7 = 6/36

We can get 11 as (5,6), (6, 5) out of 36 combinations.
So, probability to throw 11 = 2/36

Probability that the player wins on the first roll = Probability that the player throws 7 or 11
= 6/36 + 2/36 = 8/36 = 2/9

b.

Probability that the player wins on the first roll = Probability that the player throws 2 or 3

We can get 2 as (1, 1) out of 36 combinations.

So, probability to throw 2 = 1/36

We can get 3 as (2,1), (1, 2) out of 36 combinations.
So, probability to throw 3 = 2/36

Probability that the player wins on the first roll = Probability that the player throws 7 or 11
= 1/36 + 2/36 = 3/36 = 1/12

c.
If the player throws 4, the player wins on the next roll if he gets 4 on next roll.
We can get 4 as (1, 3), (2, 2) , (3, 1) out of 36 combinations.

So, probability to throw 4 = 3/36 = 1/12
If the player throws 4, probability that the player wins on the next roll = 1/12

d.

If the player throws 4, the player loses on the next roll if he gets 7 on next roll.

If the player throws 4, probability that the player wins on the next roll = 6/36 = 1/6

e.
If the player throws 4, the game ends if player wins or loses on the next roll. That is he gets 4 or 7 on next roll.
If the player throws 4, probability that the game ends on the next roll = 1/12 + 1/6 = 3/12 = 1/4