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Question

Pratik has 8 grey socks and 8 white socks.

He pulls out two socks randomly without looking at them.

What is the probability of both socks are white?


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Solution

Find the probability both the socks are white:

Given that Grey socks =8, White socks =8

Total number of socks=16

Probability of an event E is defined by PE=nEns where nE,ns are the number of favorable outcomes and the total number of possible outcomes respectively.

The probability of pulling the first sock is whitePE1=816=12

Now, Grey socks =8, White socks =7

Total number of socks remains=15

The probability of pulling the white sock isPE2=715

The probability of pulling two white socks PE=PE1×PE2

=12×715

=730

Hence, the probability of pulling two white socks is 730


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