Question

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. $\frac{1}{12}$
• D. $\frac{1}{18}$

Answer 1

The correct option is D $\frac{1}{18}$

To score 5 points, team A need to win 2 matches and draw 1 match.

Let W be the event that team A wins the game.

Let D be the event that team A draws the game.

To score 5 points, possible outcomes of 3 matches are $WWD,WDW,DWW$

Probability to score 5 points $=P\left(WWD\right)+P\left(WDW\right)+P\left(DWW\right)$

$=P\left(W\right)P\left(W\right)P\left(D\right)+P\left(W\right)P\left(D\right)P\left(W\right)+P\left(D\right)P\left(W\right)P\left(W\right)$ ...(W and D are independent events)

$=(\frac{1}{3}\times \frac{1}{3}\times \frac{1}{6})+(\frac{1}{3}\times \frac{1}{6}\times \frac{1}{3})+(\frac{1}{6}\times \frac{1}{3}\times \frac{1}{3})$

$=\frac{1}{18}$