Question

Consider a binomial experiment with

n = 7 trials

where the probability of success on a single trial is

p = 0.30.

(Round your answers to three decimal places.)


(a) Find

P(r = 0).


(b) Find

P(r ≥ 1)

by using the complement rule.

Answer 1

To find P(r = 0), use the binomial probability formula. To find P(r ≥ 1), use the complement rule.

Step-by-step explanation:

(a) To find P(r = 0), we need to calculate the probability of getting 0 successes in 7 trials. The formula for the probability of getting exactly r successes in n trials is:

P(r) = (n choose r) * p^r * (1 - p)^(n - r)

Plugging in the values, we have:

P(0) = (7 choose 0) * 0.30^0 * (1-0.30)^(7-0) = 1 * 1 * 0.7^7 = 0.0058 (rounded to three decimal places).

(b) To find P(r ≥ 1) using the complement rule, we need to calculate the probability of getting at least 1 success in 7 trials. The complement rule states that P(A') = 1 - P(A). So, P(r ≥ 1) = 1 - P(r = 0). Plugging in the value from part (a), we have:

P(r ≥ 1) = 1 - P(0) = 1 - 0.0058 = 0.9942 (rounded to three decimal places).