Question

In a box there are six envelopes each containing two cards. Three of the envelopes contain two red cards, two of them contain a red and a black card, and the last one contains two black cards. An envelope is selected at random and a card is withdrawn and found to be red. What is the chance the other card is black?

Answer 1

`(2)/(5)`

Explanation:

3 envelopes having 2 red card

2 envelopes having 1 red card and 1 black card

1 envelope having 2 black cards

We are given that . An envelope is selected at random and a card is withdrawn and found to be red.

So, No. of ways of envelope having red card = 3+2 = 5

No. of required ways of envelope having 1 red card and 1 black card = 2

So, probability of getting an envelope having 1 red card and 1 black card =
`(2)/(5)`

Hence The chance the other card is black is
`(2)/(5)`