Q269 / 270 · NDA 2016 (Phase 2) · Mathematics

In a series of 3 one-day cricket matches between teams $A$ and B of a college, the probability of team A winning or drawing are $1 / 3$ and $1 / 6$ respectively. If a win, loss or draw gives 2,0 and 1 point respectively, then what is the probability that team A will score 5 points in the series?

  • A
    $\frac{17}{18}$
  • B
    $\frac{11}{12}$
  • C
    $\frac{1}{12}$
  • Correct answer
    D
    $\frac{1}{18}$

Solution

$\begin{aligned} \text { Req. Prob. } & =\mathrm{P}(5 \text { points })=\mathrm{P}(\text { two wins and one draw }) \\ & =\mathrm{P}(\mathrm{WWD})+\mathrm{P}(\mathrm{WDW})+\mathrm{P}(\mathrm{DWW}) \\ & =\frac{1}{3} \times \frac{1}{3} \times \frac{1}{6}+\frac{1}{3} \times \frac{1}{6} \times \frac{1}{3}+\frac{1}{6} \times \frac{1}{3} \times \frac{1}{3} \\ & =\frac{1}{18}\end{aligned}$

Hence, the correct answer is option: 'D'.

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