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

a. .0554

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) = (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.