Expected number of job offers

Question

A candidate has 3 final-round interviews. They turn into offers with probabilities 0.40, 0.25, and 0.50 respectively. On average, how many job offers does the candidate receive?

Accepted Answer

Put one indicator on each interview: Xi = 1 if interview i becomes an offer. Then E[Xi] is that interview's offer probability. The number of offers is X = X1 + X2 + X3, and by linearity of expectation E[X] = 0.40 + 0.25 + 0.50 = 1.15. Takeaway. The expected number of successes is the sum of the individual success probabilities, here 0.40 + 0.25 + 0.50 = 1.15, whether or not the interviews are independent.

Expected number of job offers

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