Question

1. Desta is a gambler and regularly plays several rounds of a gamble in which he wins $6,000 if odd number of dots face up when a fair die is rolled twice and loses $2,000 for any other outcome from the two rolls of the die. In other words, the outcome of the gamble is determined by rolling a die twice on each round of the gamble and Desta wins only if odd number of dots show up on top in both rolls of the die and loses if any other outcome occurs. Desta is considering playing 18 rounds of such a gamble next week hoping that he will win back the $1,000 he lost in a similar gamble last week. If we let X represent the number of wins for Desta out of the next 18 rounds of the gamble, X will have the binomial probability distribution.

a. Please calculate the probability of success for Desta on each round of the gamble. Show how you arrived at your answer. [Hint: See the joint probability rule for independent events on slide 14 of PPT_SLIDES_SECOND_WEEK).                                           (1 point)

b. What is the probability that Desta will win none of the 18 rounds of the gamble?   (1 point)

c. What is the probability that Desta will lose at least 10 of the 18 rounds of the gamble? Show your work.                                                            (1 point)

d. What is the probability that Desta will win fewer than 8 out of the 18 rounds of the gamble? Show your work.                                                    (1 point)

e. What is the probability that Desta will lose at most 12 out of the 18 rounds of the gamble? Show your work.                                                    (1 point)

f. What is the probability that Desta will lose more than half out of the 18 rounds of the gamble?    Show your work.                                                       (1 point)                                                                                       

  g. How much money is Desta expected to win in the 18 rounds of the gamble? How much money is he expected to lose? Given your results, do you think Desta is playing a smart gamble? Please show how you arrived at your results and explain your final answer.                                                            (2 points)

h. Calculate and interpret the standard deviation for the number of wins for Desta in the next 18 rounds of the gamble. Show your work.                   (1 point)

Answer 1