In a drawer there are 4 white socks, 3 blue socks and 5 grey socks. Two socks are picked randomly. What is the possibility that both the socks are of same color?0 A. 4/11B. 1C. 2/33D. 19/66
Question
In a drawer there are 4 white socks, 3 blue socks and 5 grey socks. Two socks are picked randomly. What is the possibility that both the socks are of same color?0 A. 4/11B. 1C. 2/33D. 19/66
Solution
The total number of socks is 4 (white) + 3 (blue) + 5 (grey) = 12 socks.
The probability of drawing two socks of the same color can be calculated by adding the probabilities of drawing two white, two blue, or two grey socks.
- The probability of drawing two white socks is (4/12) * (3/11) = 1/11.
- The probability of drawing two blue socks is (3/12) * (2/11) = 1/22.
- The probability of drawing two grey socks is (5/12) * (4/11) = 5/33.
Adding these probabilities together gives the total probability of drawing two socks of the same color:
1/11 + 1/22 + 5/33 = 2/22 + 1/22 + 10/66 = 19/66.
So, the correct answer is D. 19/66.
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