A fair pair of dice is rolled
36
times. Find the probability that the same point comes up on both dice at least
11
times
P(a getting a same point onboth dice) = 6/36 = 1/6
n = 36
mean = n * p = 36 * 1/6 = 6
sd = sqrt(n * p * (1 - p))
= sqrt(36 * 1/6 * 5/6)
= 2.236
P(X > 11)
= P((X - mean)/sd > (11 - mean)/sd)
= P(Z > (11 - 6)/2.236)
= P(Z > 2.24)
= 1 - P(Z < 2.24)
= 1 - 0.9875
= 0.0125
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