Question

There are 3 blue socks, 5 brown
socks, and 4 white socks in a
drawer. If two socks are picked
up randomly, what is the
probability that the selected
socks are of the same color?
O 1
Oo
O 19/66
04/11​

Answer 1

SOLUTION

GIVEN

• There are 3 blue socks, 5 brown socks, and 4 white socks in a drawer.

• Two socks are picked up randomly

TO DETERMINE

The probability that the selected socks are of the same color

EVALUATION

Total number of socks = 3 + 5 + 4 = 12

Now two socks are picked up randomly

So total number of possible outcomes

$\displaystyle \sf{ = {}^{12}C_2 }$

$\displaystyle \sf{ = 66}$

Let A be the event that the selected socks are of the same color

Then the total number of possible outcomes for the event A is

$\displaystyle \sf{ = {}^{3}C_2 + {}^{5}C_2 + {}^{4}C_2}$

$\displaystyle \sf{ = 3 + 10 + 6}$

$\displaystyle \sf{ = 19}$

Hence the required probability

= P(A)

$\displaystyle \sf{ = \frac{19}{66} }$

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