Let -( H. T)\'o, put p-1/4 and q-3/4. and define a probability measure P on the

ID: 3353707 • Letter: L

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Let -( H. T)'o, put p-1/4 and q-3/4. and define a probability measure P on the power set of by P(w) = p#11(w)q#T(w) for each outcome w E . Think of as a space of 10 biased but independent coin flips. Calculate the probabils of each of the following events. You should use conditional probabilities and the fact that you can look at the probability space as the product of 10 iid Bernoulli(1/4) distributions to make your computations simpler. 3.2. (a) The third flip is the first H. (b) The sixth flip is the second H. (c) There are more H occurring in the first 4 flips than in the last 4 lips (d) The numberof H lips is 3 or fewer

Explanation / Answer

a) Probability that first two flips are tails and third is H. = 3/4*3/4*1/4 = 9/64

b)Probability that one Head in first 5 flips only and one heads on 6th Flip = 5C1 * (1/4)*(3/4)^4 * (1/4) = 0.0988

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Let -(H,T)10, put p = 1 /4 and q = 3/4, and define a probability measure P on th

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Let -( H. T)\'o, put p-1/4 and q-3/4. and define a probability measure P on the

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