Question

A dresser contains 4 pairs of socks, with 1 each in the colors red, black, blue, and grey. It also contains 3 skirts, with 1 each in the colors black, navy, and khaki.

What is the probability that 1 pair of red socks and 1 black skirt are chosen at random?

Answer 1

Hence the probability that 1 pair of red socks and 1 black skirt are chosen at random is
`(1)/(12)`.

Explanation:

Let A denotes the event that 1 pair of red socks are chosen.

Let B denote the event that a 1 black skirt is chosen.

let P denotes the probability of an event. ( Probability of an event is defined as the ratio of Number of favourable outcomes over the total number of outcomes)

`P(A)=(1)/(4)` and
`P(B)=(1)/(3)`

Hence, the probability that 1 pair of red socks and 1 black skirt are chosen at random i.e.
`P(A \bigcap B)` is given by:

`P(A \bigcap B)=P(A)* P(B)` (since the events are independent)

Hence,
`P(A \bigcap B)=(1)/(4)* (1)/(3)=(1)/(12)`