4. Suppose basketball player has a 90 percent chance of making a free throw. Sup

Question

4. Suppose basketball player has a 90 percent chance of making a free throw. Suppose the player starts shooting free throws. What is the probability that the player will MISS exactly 5 free throws before making one? What is the probability that the player will make exactly 10 free throws before missing three? 5. Suppose a nonstandard roulette wheel is created, with 36 slots, numbered 1 to 36, with each slot equally likely. (It is nonstandard in the sense that a typical wheel has two additional slots, numbered 0 and 00.) What is the mean and variance of the outcome of a spin of the wheel?

Explanation / Answer

4) P(missing) = 1 - 0.9 = 0.1

P(missing 5 throws before making one) = 0.15 * 0.9 = 0.000009

P(making 10 throws before missing three) = 12C10 * 0.910 * 0.12 * 0.1 = 0.023

5) E(X), mean = 1*1/36 + 2*1/36 + .. + 36*1/36 = (1 + 2 + ... + 36) / 36 = 36 * 37 / (2 * 36) = 18.5

E(X2) = 12*1/36 + 22*1/36 + .. + 362*1/36 = (12 + 22 + ... + 362) / 36 = [36 * 37 * 73] / (6 * 36) = 450.167

Var(X) = E(X2) - (E(X))2 = 450.167 - 18.52 = 107.9167

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