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 theproblem, selected at random from the book?

A can solve 90% of the problems given in a book and B can solve 70%.Wh

1.	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 theproblem, selected at random from the book?
Answer» 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.

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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 theproblem, selected at random from the book?

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