Question

Suppose that 8 cards, of which four are red, two are green and two are blue, are placed at random in 8 envelopes . Two envelops are selected at random,

1. find the probability that the envelops have red cards?
2. find the probability that they have cards of the same colors?

Answer 1

Here total cards are 8,

Red card-4

Green card-2

Blue card-2

These cards are placed at random in 8 envelopes.

Two envelopes are selected at random,

(I) find the probability that the envelops have red cards?

Solution::

Here we have 4 envelopes that's contains 4 red cards,

Let define R be the event that represent selection of envelopes have red cards.

So, we will get 2 red cards from these 4 envelopes by ways.

We can select 2 envelopes from 8 envelopes by ways.

So, the probability of getting envelopes have red cards is,

(Il) find the probability that they have cards of the same colors?

Solution::

They have cards of same colours means,

If we select 2 envelopes that's contains red cards then we get same colours.

If we select 2 envelopes that's contains green cards then we get same colours.

If we select 2 envelopes that's contains blue cards then we get same colours.

Let define events R, G and B that represents selection of 2 envelopes that's contains red, green and blue cards respectively.

Here we have 4 envelopes that's contains 4 red cards.

Here we have 2 envelopes that's contains 2 green cards.

Here we have 2 envelopes that's contains 3 green cards.

So,

We will get 2 envelopes that's contains 2 red cards by ways.

We will get 2 envelopes that's contains 2 green cards by way

We will get 2 envelopes that's contains 2 blue cards by way

So,

So, the probability of getting they have cards of same colours is,