A drawer contains 5 brown socks and 4 blue socks well mixed a man reaches the drawer and pulls out socks at random. What is the probability that they match? `4//9` b. `5//8` c. `5//9` d. `7//12`

Options

A. `4//9`
B. `5//8`
C. `5//9`
D. `7//12`

Answer

A

Explanation

Out of 9 socks, 2 can be drawn in `.^(9)C_(2)` ways. Therefore, the total number of cases is `.^(9)C_(2)`. Two socks drawn from the drawer will match if either both are brown or both are blue. Therefore, favorable number of cases is `.^(5)C_(2) + .^(4)C_(2)`. Hence, the required probability is
`=(.^(5)C_(2) + .^(4)C_(2))/(.^(9)C_(2)) = (4)/(9)`