Question

If a fair die is rolled four times,. what is the probability that two of the rolls will show '1'.

Answer 1

X ∼ B (n = 4, p = `1/6`)

q = 1 - p = 1 - `1/6 = 5/6`

`therefore P(X = x) = nC_xp^x q^(n-x)`

P(X = 2) = ⁿC₂ `(1/6)^2 (5/6)^(4-2)`

              = `6 1/6^2 xx 5^2/6^2`

             = `25/216`