Question: Total expectation calculation We have two coins, A and B. For each toss of coin A, we obtain Heads with probability 1/2; for each toss

Total expectation calculation

We have two coins, A and B. For each toss of coin A, we obtain Heads with probability 1/2; for each toss of coin B, we obtain Heads with probability 1/3. All tosses of the same coin are independent. We select a coin at random, where the probabilty of selecting coin A is 1/4, and then toss it until Heads is obtained for the first time.

The expected number of tosses until the first Heads is:

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