The mean of the numbers obtained on throwing a die having written '1' on three faces, '2' on two faces and '5' on one face is:

Step-by-step solution

The die has 6 faces in total. The distribution of numbers on the faces is as follows: Number 1 appears on 3 faces. The probability P(X=1) = 3 6 = 1 2 . Number 2 appears on 2 faces. The probability P(X=2) = 2 6 = 1 3 . Number 5 appears on 1 face. The probability P(X=5) = 1 6 . The mean E(X) of the numbers is calculated as the sum of the products of each outcome and its corresponding probability: E(X) = x_i P(x_i) = (1 1 2 ) + (2 1 3 ) + (5 1 6 ) E(X) = 1 2 + 2 3 + 5 6 Finding a common denominator of 6: E(X) = 3 6 +