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 total sock pairs

Total socks = $4 + 2 + 8 = 14$ pairs

Step2: Probability of red socks

$\text{Prob (red socks)} = \frac{\text{Red pairs}}{\text{Total pairs}} = \frac{4}{14} = \frac{2}{7}$

Step3: Calculate total hairbands

Total hairbands = $10 + 6 + 24 = 40$

Step4: Probability of red hairband

$\text{Prob (red hairband)} = \frac{\text{Red hairbands}}{\text{Total hairbands}} = \frac{10}{40} = \frac{1}{4}$

Step5: Combined probability (independent events)

$\text{Prob (both red)} = \frac{2}{7} \times \frac{1}{4} = \frac{2}{28} = \frac{1}{14}$

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 $\frac{1}{14}$.