Question

A store has 5 travel guide books and 9 fictions on the shelves. If two customers bought a book, find the probability that one of each book was bought.

Answer 1

`Probability = (45)/(98)`

Explanation:

Given

Represent travel guide with T and Fictions with F

`T = 5`

`F = 9`

Required

Determine the probability that one of both was selected

This implies that (1 travel guide and 1 fiction) or (1 fiction and 1 travel guide)

The probability is is calculated as thus:

`Probability = P(T\ n\ F)\ or\ P(F\ n\ T)`

In probability, the above formula can be translated to

`Probability = P(T) *P(F)\ +\ P(F) *P(T)`

`Probability = (n(T))/(Total) *(n(F))/(Total)\ +\ (n(F))/(Total) *(n(T))/(Total)`

`Probability = (5)/(5 + 9) *(9)/(5 + 9) +(9)/(5 + 9) *(5)/(5 + 9)`

`Probability = (5)/(14) *(9)/(14) +(9)/(14) *(5)/(14)`

`Probability = (45)/(196) +(45)/(196)`

`Probability = (90)/(196)`

`Probability = (45)/(98)`