In a certain game, Ravi beats Pawan with probability 2/5. They play a series of games until one of them wins six games. Assume that each game is independent of the other. Find the probability that the series will end after 10 games
Answers
Given : In a certain game, Ravi beats Pawan with probability 2/5.
They play a series of games until one of them wins six games.
Assume that each game is independent of the other.
To Find : the probability that the series will end after 10 games
Solution:
Series will end after 10 games
if 6th games is won by Either ravi or pawan and same person has already won 5 games out of 9 games
6th game Ravi won + 6th game Pawan won
= (2/5) ⁹C₅ (2/5)⁵(3/5)⁴ + (3/5) ⁹C₅ (3/5)⁵(2/5)⁴
⁹C₅ and ⁹C₄ are same thing so any one can be taken
= ⁹C₅ (2/5)⁴ (3/5)⁴ ( (2/5)² + (3/5)²)
= 126 * (1296/ 5⁸) ( 13/5²)
= 0.2173796352
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