Probability Grumps

Probability Level 3

The probability that Danny wins a game is twice the probability that Arin wins a game. If each game is independent (that is, the outcome of one game does not affect another), the probability that Danny wins exactly two games out of five is a b \frac{a}{b} where a a and b b are relatively prime positive integers.

Find a + b . a+b.


The answer is 283.

Sean Roberson by Sean Roberson , 27, USA

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1 solution

Rohit Sachdeva
Sep 19, 2014

Let us assume there is no draw in a game.

So, in 1 game,

P(Danny win)=2/3

P(Arun win)=1/3

In 5 games,

P(Danny-2, Arun-3)=5C2 (2/3)²(1/3)³

=40/243=a/b

a+b=283

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