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Probability -Gravner- 48

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A chocolate egg either contains a toy or is empty. Assume that each egg contains a toy with probability p, independently of other eggs. You have $5$ eggs; open the first one and see if it has a toy inside, then do the same for second one, etc. Let E1 be the event that you get at least $4$ toys and let E2 be the event that you get at least two toys in succession. Compute P(E1) and P(E2) . Are E1 and Ee independent?

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