Question

Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40%. Round to the nearest tenth of a percent.

Answer 1

7.7

I did the math and the answer to this question is 7.7%

Answer 2

Answer: Probability of exactly four success is 0.01536.

Explanation:

Since we have given that

Number of trails = 5

Probability of success is given by

`40\%=0.4`

Probability of failure is given by

`1-0.4=0.6`

Number of success = 4

As we know the formula for "Binomial distribution":

`P(X=x)=^nC_xp^(n-x)q^x\\\\Here,\\\\\text{ p denotes probability of success}\\\\\text{q denotes probability of failure}`

So, it becomes,

`P(X=4)=^5C_4(0.4)^4(0.6)\\\\P(X=4)=1* 0.4^4* 0.6\\\\P(X=4)=0.01536`

Hence , Probability of exactly four success is 0.01536.