Question

A die is rolled five times and a 5 or 6 is considered a success. Find the probability of

(i) at least 2 successes,
(ii) at least one but no more than 3 successes.

Answer 1

(i) The probability of at least 2 successes is 0.2093.

(ii) The probability of at least one but no more than 3 successes is 0.9548.

Explanation:

Now the total number of cases = {1, 2, 3, 4, 5, 6} = 6.

Favourable cases = {1, 6} = 2.

`p = \frac{2} {3} = \frac{1} {3} \\\\q = 1- p\\\\q = (2)/(3) \\\\n=5`

i) at least 2 successes,

`P(X\geq 2) = (^(n)C_(x) )* p^(x) * (1-p)^(n-x)\\\\P(X\geq 2) = 0.2093`

ii) at least one but no more than 3 successes,

`P(X\leq 3) = (^(n)C_(x) )* p^(x) * (1-p)^(n-x)\\\\P(X\leq 3)= 0.9548`