Answer to Question #91979 in Statistics and Probability for samman

Question

Suppose that a dice is rolled four times. We assume that the outcomes are independent and the dice is fair. Find the probabilities of 0, 1, 2, 3 and 4 sixes.

Answer 1

0 six: P = (5/6)*(5/6)*(5/6)*(5/6) = 625 / 1296

1 six: P = (1/6)*(5/6)*(5/6)*(5/6)*С₄¹ = 125 * 4 / 1296 = 125 / 324

2 sixes: P = (1/6)*(1/6)*(5/6)*(5/6)*C₄² = 25 * 6 / 1296 = 25 / 216

3 sixes: P = (1/6)*(1/6)*(1/6)*(5/6)*C₄³ = 5 *4 / 1296 = 5 / 324

4 sixes: P = (1/6)*(1/6)*(1/6)*(1/6) = 1 / 1296