Question

a laundry basket contains 8 white t - shirts and 6 black t - shirts. what is the probability of randomly picking 2 black socks from the basket?

Explanation:

Step1: Calculate total number of t - shirts

The basket has 8 white t - shirts and 6 black t - shirts. So the total number of t - shirts is $8 + 6=14$.

Step2: Calculate probability of first black t - shirt

The probability of picking the first black t - shirt is $\frac{6}{14}$.

Step3: Calculate probability of second black t - shirt

After picking one black t - shirt, there are 5 black t - shirts left and 13 t - shirts in total. So the probability of picking the second black t - shirt is $\frac{5}{13}$.

Step4: Calculate combined probability

The probability of picking 2 black t - shirts is the product of the probabilities of picking each black t - shirt. So $P=\frac{6}{14}\times\frac{5}{13}=\frac{30}{182}=\frac{15}{91}$.

Answer:

$\frac{15}{91}$