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 `E_(1)=` event that A solves the problem,
and `E_(2)=` event that B solves the problem.
Then, `P(E_(1))=90/100=9/10` and `P(E_(2))=70/100=7/10`.
Clearly, `E_(1)` and `E_(2)` are independent events.
`:. P(E_(1) nn E_(2))=P(E_(1))xxP(E_(2))=(9/10xx7/10)=63/100`.
`:.` P(at least one of them will solve the problem)
`=p(E_(1) uu E_(2))`
`=P(E_(1))+P_(E_(2))-P(E_(1) nn E_(2))`
`=(9/10+7/10-63/100)=((90+70-63))/100=97/100`.
Hence, the required probability is 0.97.