What is the probability of 4 successes for a binomial

toofehblf

toofehblf

Answered question

2022-02-12

What is the probability of 4 successes for a binomial experiment consisting of 11 trials with probability 0.4 of success on each trial?

Answer & Explanation

Morgan Griffin

Morgan Griffin

Beginner2022-02-13Added 9 answers

Step 1
Xb(n, p) where n=11 and p=0.4
and we are looking for P(X=4)
Since
Xb(n, p)P(X=k)=(Cn, k)pk(1p)nk
where Cn, k=n!k!(nk)!
we have to calculate
P(X=4)=11!4!(114)!(0.4)4(0.6)7
=11!4!(7!)(0.4)4(0.6)7=(8)(9)(10)(11)4!(0.0256)(0.0279936)
=2(9)(10)(11)3!(0.0256)(0.0279936)=(2)(3)(10)(11)2!(0.0256)(0.0279936)
=330(0.0256)(0.0279936)0.237

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