Question

1) In a dice game where the player rolls two dice, a prize is awarded if the player rolls a 2, 3, 11, or 12.

a. What is the probability that a player will win a prize in the first 5 tries?

b. What is the expected number of games until the player wins a prize?

2) Suppose that last year a local girl scouts group sold one box of cookies to a household with probability 0.45.

a. If this trend continues this year, what is the probability that they visit at most 5 houses to sell 3 boxes?

b. If they want to sell 100 boxes, how many houses should they expect to have to visit?

Thank you for the help.

Answer 1

a)

here P(winning)=P(player rolls 2)+P(player rolls 3)+P(player rolls 11)+P(player rolls 12)

=(1/36)+(2/36)+(2/36)+(1/36)=1/6

hence probability that a player will win a prize in the first 5 tries =1-P(player not wins in first 5 attemts)

=1-(1-1/6)⁵ =0.598122

b) expected number of games until the player wins a prize =1/p=1/(1/6)=6

2)

probability that they visit at most 5 houses to sell 3 boxes =1-P(till 5 houses sold at most 2 boxes)

=1-(P(X=0)+P(X=1)+P(X=2))

=1-

=1-0.0503-0.2059-0.3369 =0.4069

b)

expectred to visit houses=r/p=100/0.45=222.22