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

Answer:

$Probability = \frac{45}{98}$

Step-by-step 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

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

$Probability = \frac{n(T)}{Total} *\frac{n(F)}{Total}\ +\ \frac{n(F)}{Total} *\frac{n(T)}{Total}$

$Probability = \frac{5}{5 + 9} *\frac{9}{5 + 9} +\frac{9}{5 + 9} *\frac{5}{5 + 9}$

$Probability = \frac{5}{14} *\frac{9}{14} +\frac{9}{14} *\frac{5}{14}$

$Probability = \frac{45}{196} +\frac{45}{196}$

$Probability = \frac{90}{196}$

$Probability = \frac{45}{98}$