Answer to Question #157284 in Statistics and Probability for Vincent Miyato

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

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