Question

according to the tree diagram below what is the probability that someone buys a book that is paperback and fiction

Answer 1

see the attached figure to better understand the problem

we know that

`0.65\ (65\%)` of the buyers buy paperback and
`0.45\ (45\%)` of them buy fiction.

Hence

The probability that they buy both fiction and paperback is equal to

`0.65*0.45=0.2925`

the answer is

`0.2925`

Answer 2

Let us check out the diagram. The probability that a person buys a paperback is 0.65. The next leafs of the diagram (to the right of choosing paperback) show two events: the event that the buyer who has bought a paperback buys fiction and the probability he buys non-fiction. So 65% of the buyers buy paperback and 0.45 (=45%) of them buy fiction. Hence the probability that they buy both fiction and paperback is 0.65*0.45=0.2925. This is always a helpful thought procedure with such exercises; we can solve the same way for hardcover non-fiction etc.