Unformatted text preview: STAT 100A HWII Due next Wed
Problem 1: If we ﬂip a fair coin n times independently, what is the probability that we observe k heads? k = 0, 1, ..., n. Please explain your answer. Problem 2: Prove the following two identities: ¯ (1) P (AB ) = 1 − P (AB ). (1) P (A ∩ B C ) = P (AB ∩ C )P (B C ). Problem 3: Independence. If P (AB ) = P (A), prove (1) P (A ∩ B ) = P (A)P (B ). (2) P (B A) = P (B ). Problem 4: Suppose an urn has r red balls and b black balls. We randomly pick a ball. Then we put 3 balls of the same color back to the urn. Then we randomly pick a ball again. What is the probability that the second pick is red? 1 ...
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 Winter '10
 CRISTOU
 Probability, Following, ball, STAT 100A HWII

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