Question

A box contains 6 black socks and 4 red socks. What is the probability of picking two black socks from the bag without replacement? What is the answer in simplest form?

Answer 1

9/25

Explanation:

Our box contains 10 socks. (6, which are black and 4 which are red)

Probability of picking 1 black sock will be 6/10

Number of ways it can occur / Total number of outcomes.

In this question we pick two socks, one black firstly and another black, in the second turn. When we say AND, it means intersection

P (B₁ ∩ B₂) = 6/10 . 6/10

When the events are independent, the probability of the intersection will be the product of the probabilities,

P (B₁ ∩ B₂) = 36/100 = 9/25