Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability...

Question

Question

Problem 1 (10 points). If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exa

Answer 1

Answer #1

Binomial distribution: P(X) = nCx p^x q^n-x

P(success), p = P(at least one of the two dice is 6)

= 1 - P(both dice are not showing 6)

= 1 - (5/6)²

= 0.3056

q = 1 - p = 0.6944

Number of trials, n = 10

P(at least one 6 in exactly 5 of these 10 rolls) = P(X = 5)

= 10C5 x 0.3056⁵ x 0.6944⁵

= 0.1084

Answer 2

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