Suppose the probability for A to win game B is 0.4

Question

Suppose the probability for A to win game B is 0.4. If A has an option of playing either a “best of 3 games” of a “best of 5 games” match against B, which option should be choose so that the probability of his winning the match is higher? (No game ends in a draw).

Jitender Pal · Accepted Answer

Hello Student,

Please find the answer to your question

The probability p₁ (say) of winning the best of three games is = the prob. of winning two games + the prob. of winning three games.

= ³ C₂ (0.6) (0.4)² + ³ C₃ (0.4)³ [Using Binomial distribution]

Similarly the probability of winning the best five games is p₂ (say) = the prob. of winning three games + the prob. of winning 5 games.

= ⁵ C₃ (0.6)² (0.4)³ + ⁵ C₃ (0.6) (0.4)³ + ⁵ C₅ (0.4)⁵

We have p₁ = 0.288 + 0.064 = 0.352

And p₂ = 0.2304 + 0.0768 + 0.01024 = 0.31744

As p₁ > p₂

∴ A must choose the first offer i.e. best of three games.

Thanks
Jitender Pal
askIITians Faculty

Algebra> Suppose the probability for A to win game...

Suppose the probability for A to win game B is 0.4. If A has an option of playing either a “best of 3 games” of a “best of 5 games” match against B, which option should be choose so that the probability of his winning the match is higher? (No game ends in a draw).

Hrishant Goswami , 11 Years ago

Jitender Pal

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Algebra> Suppose the probability for A to win game...

Suppose the probability for A to win game B is 0.4. If A has an option of playing either a “best of 3 games” of a “best of 5 games” match against B, which option should be choose so that the probability of his winning the match is higher? (No game ends in a draw).

Hrishant Goswami , 11 Years ago

Jitender Pal

LIVE ONLINE CLASSES

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