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Find the probability of at least one

failure in five trials of a binomial
experiment in which the probability of
success is 30%.
Round to the nearest tenth of a
percent.

User Jeremy Jay
by
8.0k points

1 Answer

3 votes

Answer:

99.8% probability of at least one failure.

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.

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.

User Hatzegopteryx
by
7.5k points

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