Question

olga has a drawer of socks with 4 red pairs, 2 gray pairs, and 8 black pairs. she also has a bag of hairbands with 10 red, 6 gray, and 24 black hairbands. if she selects randomly, what is the probability that olga will select a red pair of socks and a red hairband? click the arrows to choose an answer from each menu. the probability that olga will randomly select a red pair of socks is choose_, and the probability that she will randomly select a red hairband is choose_. the probability that she will select a red pair of socks and a red hairband is choose_.

Explanation:

Step1: Calculate sock probability

Find ratio of red socks pairs to total pairs. $\frac{4}{4 + 2+8}$

Step2: Calculate hair - band probability

Find ratio of red hair - bands to total hair - bands. $\frac{10}{10 + 6+24}$

Step3: Calculate combined probability

Multiply sock and hair - band probabilities. $\frac{2}{7}\times\frac{1}{4}$

Answer:

The probability that Olga will randomly select a red pair of socks is $\frac{4}{4 + 2+8}=\frac{4}{14}=\frac{2}{7}$, and the probability that she will randomly select a red hair - band is $\frac{10}{10 + 6+24}=\frac{10}{40}=\frac{1}{4}$. The probability that she will select a red pair of socks and a red hair - band is $\frac{2}{7}\times\frac{1}{4}=\frac{2}{28}=\frac{1}{14}$.