Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is

Step-by-step solution

There are only two outcomes, success which stands for getting either 3 or 5, and failure, stands for getting any other outcome. Probability for success = p = 2 6 Probability for failure = q = 4 6 Number of trials = n = 27 Number of dice = 4 Using Binomial Probability, P(at least 2 shows 3 or 5) = C 2 4 · 2 6 2 4 6 2 + C 3 4 2 6 3 4 6 + C 4 4 2 6 4 = 384 + 128 + 16 6 4 = 11 27 Expectation is numerically same as mean. ∴ expectation = n p = 27 · 11 27 = 11