1. Desta is a gambler and regularly plays several rounds of agamble in which he wins $6,000 if odd number of dots face up when afair die is rolled twice and loses $2,000 for any other outcomefrom the two rolls of the die. In other words, the outcome of thegamble is determined by rolling a die twice on each round of thegamble and Desta wins only if odd number of dots show up on top inboth rolls of the die and loses if any other outcome occurs. Destais considering playing 18 rounds of such a gamble next week hopingthat he will win back the $1,000 he lost in a similar gamble lastweek. If we let X represent the number of wins for Desta out of thenext 18 rounds of the gamble, X will have the binomial probabilitydistribution.

a. Please calculate the probability ofsuccess for Desta on each round of the gamble. Show how you arrivedat your answer. [Hint: See the joint probabilityrule for independent events on slide 14 ofPPT_SLIDES_SECOND_WEEK).                                          (1point)

b. What is the probability that Destawill win none of the 18 rounds of thegamble?   (1 point)

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

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

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

f. What is the probability that Destawill lose more than half out of the 18 rounds ofthe gamble?    Show yourwork.                                                      (1point)                                                                                      

  g. How much money is Destaexpected to win in the 18 rounds of the gamble? How much money ishe expected to lose? Given your results, do you think Desta isplaying a smart gamble? Please show how you arrived at your resultsand explain your finalanswer.                                                         (2 points)

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