Question

Let the probability of success on a Bernoulli trial be 0.30. a. In five Bernoulli trials, what is the probability that there will be 4 failures? (Do not round intermediate calculations. Round your final

Answer 1

36.01% probability that there will be 4 failures.

Explanation:

A sequence of Bernoulli trials is the binomial probability distribution.

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.

In this problem, we have that:

`n = 5, p = 0.3`

a. In five Bernoulli trials, what is the probability that there will be 4 failures?

This is 4 failures and 5-4 = 1 success

This is P(X = 1).

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 1) = C_(5,1).(0.3)^(1).(0.7)^(4) = 0.3601`

36.01% probability that there will be 4 failures.