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  4. 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. The probability that A wins is

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Q. 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. The probability that $A$ wins is

Probability - Part 2

Solution:

For A to win, A can drawn either 3,6 or 5,6 . If A draws 3,6 then B can draw only 8 and 9 . Probability $=\left(\frac{1}{3}\right)\left(\frac{1}{3}\right)=\frac{1}{9}$.
Also, if A draws 5, 6 then B can draw, any two probability $=\frac{1}{3} \times 1=\frac{1}{3}$
So, required probability $=\frac{1}{9}+\frac{1}{3}=\frac{4}{9}$.