Question

Find the probability of at least one

Answer 1

Answer:

99.8% probability of at least one failure.

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.

Probability of success is 30%.

This means that $p = 0.3$

Five trials:

This means that $n = 5$

Find the probability of at least one failure in five trials of a binomial experiment in which the probability of success is 30%.

Less than five sucesses, which is:

$P(X < 5) = 1 - P(X = 5)$

In which

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

$P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.002$

$P(X < 5) = 1 - P(X = 5) = 1 - 0.002 = 0.998$

0.998*100% = 99.8%

99.8% probability of at least one failure.