Question

trey has 6 black socks and 4 white socks in a drawer. what is the probability of randomly pulling out 1 black sock, then a 2nd black sock (without replacement)?

Explanation:

Step1: Calculate total number of socks

There are 6 black and 4 white socks, so total = 6 + 4=10 socks.

Step2: Calculate probability of first - black sock

The probability of pulling a black sock first is $\frac{6}{10}$ since there are 6 black socks out of 10 total socks.

Step3: Calculate probability of second - black sock

After pulling one black sock without replacement, there are 5 black socks left and 9 total socks left. So the probability of pulling a second black sock is $\frac{5}{9}$.

Step4: Calculate combined probability

Since these are sequential events, we multiply the probabilities. So the probability is $\frac{6}{10}\times\frac{5}{9}=\frac{30}{90}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$