Chapter 9.2, Problem 67HP

To determine

Tofind: the probability that a senior’s ticket will be chosen.

Answer to Problem 67HP

The probability that a senior’s ticket will be chosen is $\frac{3}{8}$ .

Explanation of Solution

Given information:

Seniors $=100$ , juniors $=150$ , sophomores $=200$ .

The drawing will contain $3$ tickets for each senior name, $2$ for each junior and $1$ for each sophomore.

Calculation: to find the probability, divide the total senior tickets by the total tickets,

  $\begin{array}{l}\text{probability}=\frac{3·100}{3·100+2·150+1·200}\\ \text{probability}=\frac{300}{800}\text{ [multiply and add]}\\ \text{probability}=\frac{3}{8}\text{ [simplify]}\end{array}$

Thus, the probability is $\frac{3}{8}$ .