Question

question 8
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

Explanation:

Step1: Calculate total number of socks

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

Step2: Calculate probability of first - sock being red

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

Step3: Calculate probability of second - sock being red

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

Step4: Calculate probability of both socks being red

Using multiplication rule for independent events (in the sense of sequential selection without replacement), probability = $\frac{6}{16}\times\frac{5}{15}$
$=\frac{6\times5}{16\times15}=\frac{30}{240}=\frac{1}{8}$

Answer:

$\frac{1}{8}$