Question

An author has prepared to submit six books for publication. The probability of any book being accepted is 0.20, assuming independence, find the probability that the author will have:

(i) Exactly one book accepted.

(ii) At least two books accepted.

(iii) At most two books accepted.

Answer 1

This is a binomial distribution with n=6, p=0.2.

(i) $P(X=1)=C_6^10.2^1(1-0.2)^5=0.3932.$

(ii) $P(X\ge2)=1-P(X=0)-P(X=1)=C_6^00.2^0(1-0.2)^6+C_6^10.2^1(1-0.2)^5=$

$=0.3446.$

(iii) $P(X\le2)=P(X=0)+P(X=1)+P(X=2)=$

$=C_6^00.2^0(1-0.2)^6+C_6^10.2^1(1-0.2)^5+C_6^20.2^2(1-0.2)^4=0.9011.$