Question

4 multiple choice 1 point
at an ice skating rink, $\frac{3}{5}$ of the skaters were teenagers, $\frac{2}{3}$ of whom were wearing gloves. of the teenagers wearing gloves, 10 percent also wore hats. if a skater is chosen at random, what is the probability that skater is a teenager wearing both a hat and gloves?
$\frac{1}{10}$
$\frac{1}{15}$
$\frac{2}{5}$
$\frac{1}{25}$

Explanation:

Step1: Find teen glove wearers

$\frac{3}{5} \times \frac{2}{3} = \frac{6}{15} = \frac{2}{5}$

Step2: Find teen hat+glove wearers

$\frac{2}{5} \times 0.1 = \frac{2}{5} \times \frac{1}{10} = \frac{2}{50} = \frac{1}{25}$

Answer:

$\frac{1}{25}$ (corresponding to the last option)