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belka [17]
3 years ago
15

Let the probability of success on a Bernoulli trial be 0.30. a. In five Bernoulli trials, what is the probability that there wil

l be 4 failures? (Do not round intermediate calculations. Round your final
Mathematics
1 answer:
olga_2 [115]3 years ago
8 0

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.

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