Multiple choice

'm' red socks and '10' blue socks are in a drawer. If two socks are taken out at random, the chance that they have the same colour is 9/19. What is the value of m?

  1. 6

  2. 8

  3. 10

  4. 15

  5. 20
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C Correct answer
AI explanation

The probability of drawing two socks of the same color combines the chances of picking two red socks and two blue socks. Using the combination formula, this probability is given by (mC2 + 10C2) divided by (m + 10)C2, which equals 9/19. If we test m = 10, the total socks become 20, and the probability calculates to (45 + 45) divided by 190, equaling 90/190 or 9/19, confirming the value of m is 10.

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