Question

What is the probability that if a pair of dice is rolled eighteen times, exactly three sums of seven are rolled? (Round your answer to four decimal places.)

Answer 1

Number of times a pair of dice rolled : n =18

p : Probability of sum of seven when a pair dice rolled

when a pair dice rolled:

Total number of outcomes = 6 x 6 =36

Outcomes that favor Sum of Seven : (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Number of outcomes that favor Sum of Seven = 6

Probability of sum of seven when a pair dice rolled

= Number of outcomes that favor Sum of Seven/Total number of outcomes = 6/36 =1/6

X : Number of times sum of seven are rolled

X follows Binomial distribution with n= 18 and p

Probability mass function of X is given

Probability that 'r' sum of sevens are rolled = P(X=r)

probability that if a pair of dice is rolled eighteen times, exactly three sums of seven are rolled = P(X=3)

probability that if a pair of dice is rolled eighteen times, exactly three sums of seven are rolled = 0.2452