a fair die is rolled 8 times. Find: (Please give an explanation for both answers. I'm unsure how to approach the questions)
b) what is the probability the die lands on an odd number at least 2 times
c) what is the probability the die lands on a 6 at most twice
b) P(landing an odd number) = Number of odd numbers / Total number of faces
= 3/6
= 0.5
The die is rolled 8 times
So, this is a binomial distribution with n = 8
P(odd number), p = 0.5
and q = 1 - p = 0.5
P(X) = nCx pxqn-x
P(lands on an odd number at least 2 times) = P(X
2)
= 1 - P(X < 2)
= 1 - P(0) - P(1)
= 1 - 0.58 - 8C1x0.5x0.57
= 0.9648
c) P(landing on 6), p = 1/6
q = 1 - 1/6 = 5/6
n = 8
P(die lands on a 6 at most twice) = P(X
2)
= P(0) + P(1) + P(2)
= (5/6)8 + 8C1x(1/6)x(5/6)7 + 8C2x(1/6)2x(5/6)6
= 0.2326 + 0.3721 + 0.2605
= 0.8652
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