Question

A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them will solve the problem, selected at random from the book ?

Answer 1

Let

P(A) = 90/100; P(B) = 70/100 

∴ Probability of at least solving by one 

= P( \(\bar{A}\)B) + P(A \(\bar{B}\)) + P(AB) 

= P(\(\bar{A}\) B) x P(B) + P(\(\bar{A}\))P( \(\bar{B}\)) + P(A) x P(B)

= [1 – P(A)] x P(B) + P(A) [1 – P(B)] + P(A) x P(B)]