Question

Consider a binomial experiment with n = 5 trials where the probability of success on a single trial is p = 0.30. (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.

Answer 1

0.16807 ; 0.83193

Explanation:

Given that:

Number of trials, n = 5

Probability of success, p = 0.30

P(r = 0)

Using the binomial probability relation :

P(x =r) = nCr * p^r * (1 - p)^(n - r)

(a) Find P(r = 0).

P(r = 0) = 5C0 * 0.3^0 * (0.7)^(5- 0)

= 1 * 1 * 0.16807

= 0.16807

(b) Find P(r ≥ 1) by using the complement rule

P(r ≥ 1) = 1 - P(r = 0)

P(r ≥ 1) = 1 - 0.16807

P(r ≥ 1) = 0.83193