Question

question 8
2 pts
your drawer contains 6 red socks and 10 blue socks. its too dark to see which are which, but you grab two anyway. what is the probability that both socks are red? write your answer as a fraction
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Explanation:

Step1: Calculate total number of socks

Total socks = 6 (red) + 10 (blue) = 16.

Step2: Calculate probability of first - red sock

Probability of first red sock = $\frac{6}{16}$.

Step3: Calculate probability of second - red sock

After picking one red sock, there are 5 red socks left and 15 total socks left. So probability of second red sock = $\frac{5}{15}$.

Step4: Calculate probability of both red socks

Using the multiplication rule for independent events (in this case, sequential draws without replacement), probability that both are red = $\frac{6}{16}\times\frac{5}{15}$.
$\frac{6}{16}\times\frac{5}{15}=\frac{6\times5}{16\times15}=\frac{30}{240}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$