Question

In a binomial experiment, the probability of success is .06. What is the probability of two successes in seven trials? a. .0554 b. .28 c. .0036 d. .06

Answer 1

Answer:

a. .0554

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability of success is .06.

This means that $p = 0.06$

What is the probability of two successes in seven trials?

This is P(X = 2) when n = 7. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{7,2}.(0.06)^{2}.(0.94)^{5} = 0.054$

The correct answer is given by option a.