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 sock - probability

Find total number of sock pairs: $4 + 2+8=14$. Probability of red sock pair $P(\text{red sock})=\frac{4}{14}=\frac{2}{7}$.

Step2: Calculate hair - band probability

Find total number of hair - bands: $10 + 6+24 = 40$. Probability of red hair - band $P(\text{red hair - band})=\frac{10}{40}=\frac{1}{4}$.

Step3: Calculate combined probability

Since the events are independent, use $P(A\cap B)=P(A)\times P(B)$. So $P(\text{red sock and red hair - band})=\frac{2}{7}\times\frac{1}{4}=\frac{2}{28}=\frac{1}{14}$.

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 $\frac{1}{14}$.