Question

A fair cubical die is thrown twice and their scores summed up. If the sum of the scores of upper side faces by throwing two times a die is an event. Find the Expected Value of that event.

(a) 48

(b) 76

(c) 7

(d) 132

I have been asked this question during an internship interview.

My question is taken from Discrete Probability topic in division Discrete Probability of Discrete Mathematics

Answer 1

Correct choice is (c) 7

The best I can explain: Sample space = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.Suppose: P(2) = \(\frac{1}{36}\), P(3) = \(\frac{2}{36}\), P(4) = \(\frac{3}{36}\), P(5) = \(\frac{4}{36}\), P(6) = \(\frac{5}{36}\), P(7) = \(\frac{6}{36}\), P(8) = \(\frac{5}{36}\), P(9) = \(\frac{4}{36}\), P(10) = \(\frac{3}{36}\), P(11) = \(\frac{2}{36}\) and P(12) = \(\frac{1}{36}\). Now, Expected Value:

μ = E(A) = ∑x * P(x) = \(2 * \frac{1}{36} + 3 * \frac{2}{36} + 4 * \frac{3}{36} + 5 * \frac{4}{36} + 6 * \frac{5}{36} \)

\(+ 7 * \frac{6}{36} + 8 * \frac{5}{36} + 9 * \frac{4}{36} + 10 * \frac{3}{36} + 11 * \frac{2}{36} + 12 * \frac{1}{36} = \frac{252}{36}\) = 7.