Probability of at least one success in n trials

Asked by maham237 @ 09/01/2021 in Mathematics viewed by 276 People

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.

Answered by maham237 @ 09/01/2021

Answer:

0.99757

Step-by-step explanation:

The probability of success is 30% =0.3

Since we know that the sum of probabilities is 1

So, The probability of failure = 1-0.3 = 0.7

We are supposed to find the probability of at least one failure in five trials of a binomial experiment

Binomial expression : $P(X)=^nC_r p^r q ^{(n-r)}$

where p is the success

q is the failure

r is the favorable trial

n = total trials

So, total trials = n = 5

In this case the success is getting failure is the succes

So, p =0.7

q =0.3

So,The probability of at least one failure in five trials:

$1-^5C_0 (0.7)^0 (0.3) ^{5}$

$1- (0.3) ^{5}$

$0.99757$

Thus the probability of at least one failure in five trials of a binomial experiment is 0.99757

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