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BITSAT 2013
Exam
BITSAT
Year
2013
Subject
Mathematics
Chapter
Probability

BITSAT 2013 · Mathematics · Probability

The probability of India winning a test match against West Indies...

The probability of India winning a test match against West Indies is 1/21 / 2. Assuming independence from match to match, the probability that in a 5 match series India's second win occurs at the third test, is -

Options

  1. A2/32 / 3
  2. B1/21 / 2
  3. C1/41 / 4
  4. D1/81 / 8

Correct answer

C. 1/41 / 4

Step-by-step solution

The sample space is [LWW, WLW] \therefore P(LWW)+P(WLW)=\mathrm{LWW})+\mathrm{P}(\mathrm{WLW}) = Probability that in 5 match series, it is India's second win =P(L)P(W)P(W)+P(W)P(L)P(W)=18+18=28=14\begin{array}{l} = P(\mathrm{ L}) \mathrm{P}(\mathrm{W}) \mathrm{P}(\mathrm{W})+\mathrm{P}(\mathrm{W}) \mathrm{P}(\mathrm{L}) \mathrm{P}(\mathrm{W})\\ =\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4} \end{array}
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