olga has a drawer of socks with 4 red pairs, 2 gray pairs, and 8 black pairs. she also has a bag of…

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...

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...

Answer

Explanation:

Step1: Calculate total number of sock - pairs

Total number of sock - pairs is $4 + 2+8=14$ pairs.

Step2: Calculate probability of selecting red sock - pair

The probability of selecting a red pair of socks, $P(\text{red socks})=\frac{4}{14}=\frac{2}{7}$.

Step3: Calculate total number of hair - bands

Total number of hair - bands is $10 + 6+24 = 40$ hair - bands.

Step4: Calculate probability of selecting red hair - band

The probability of selecting a red hair - band, $P(\text{red hairband})=\frac{10}{40}=\frac{1}{4}$.

Step5: Calculate probability of both events

Since the events of selecting a sock and a hair - band are independent, the probability of selecting a red pair of socks and a red hair - band is $P = P(\text{red socks})\times P(\text{red hairband})=\frac{2}{7}\times\frac{1}{4}=\frac{2}{28}=\frac{1}{14}$.

Answer:

The probability that Olga will randomly select a red pair of socks is $\frac{2}{7}$, and the probability that she will randomly select a red hairband is $\frac{1}{4}$. The probability that she will select a red pair of socks and a red hairband is $\frac{1}{14}$.