Independent solution

How to solve this Binomial Distribution question

Setup

Setup

Count no-accident months among the first seven months. Independence and the 0.40 monthly no-accident probability give a binomial count.

X=#{no-accident months among the first seven},X∼Bin⁡(7,0.40)X=\#\{\text{no-accident months among the first seven}\},\qquad X\sim\operatorname{Bin}(7,0.40)

Model

Model

The target event is equivalent to observing at least four no-accident months in those seven trials.

Pr⁡(target)=Pr⁡(X≥4)\Pr(\text{target})=\Pr(X\ge4)

Compute

Compute

Adding the binomial masses from four through seven gives 0.289792.

∑k=47(7k)(0.4)k(0.6)7−k=0.289792\sum_{k=4}^{7}\binom7k(0.4)^k(0.6)^{7-k}=0.289792

Answer

Answer

The required binomial upper-tail probability is approximately 0.29, selecting choice D.

0.29(D)\boxed{0.29\quad\text{(D)}}