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

Answer:

36.01% probability that there will be 4 failures.

Step-by-step 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.

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

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.