Question

According to a survey by MANCOSA, 34% of Capitec Bank employees resign because of poor pay, 28% resign because of a career change, while the remainder resign due to family commitments. Determine the following probabilities (for a group of seven resigned employees)
4.2.1 Three resigned due to poor pay. (3)
4.2.2 Four resigned due to family commitments.

Answer 1

4.2.1. Binomial distribution with $p=0.34,\;n=7$ .

$P(X=3)=C_7^3p^3(1-p)^4=\frac{7!}{3!4!}*0.34^3*0.66^4=0.2610.$

4.2.2. Binomial distribution with $p=1-0.34-0.28=0.38,\;n=7.$

$P(X=4)=C_7^4p^4(1-p)^3=\frac{7!}{4!3!}*0.38^4*0.62^3=0.1739.$