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KVPY2011MathematicsProbability

Two players play the following game : A writes 3,5,6 on three different cards ; B writes 8,9,10 on three different cards. Both draw randomly two cards from their collections. Then A computes the product of two numbers he/she has drawn, and B computes the sum of two numbers he/she has drawn. The player getting the larger number wins. What is the probability that A wins?

Options

  1. A1 3
  2. B5 9
  3. C4 9
  4. D1 9

Correct answer

C. 4 9

Step-by-step solution

For A to win, A can draw either 3,6 or 5,6 . If A draws 3,6 then B can draw only 8 & 9 Prob. = 1 3 1 3 = 1 9 If A draws 5,6 then B can draw, any two array l Probability = 1 3 1= 1 3 Probability = 1 9 + 1 3 = 4 9 array

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