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Question

A and B having equal skill, are playing a game of best of 5 points. After A has won two points and B has won one point, the probability that A will win the game is:


A

1/2

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B

2/3

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C

3/4

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D

None

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Solution

The correct option is C

3/4


Let us say that each box corresponds to a point in the game:first box to first point, 2nd box to

second point. And so on.

Now, let us assume that the first two points were won by A and the third by B. The other orders

does not matter because we are considering only the number of wins to decide who won, not

the order

Case I: When A gets the fourth point,

There are two possibilities for 5th point, either A or B gets it

- A wins

- B wins

Case 2: when B gets the fourth point, there are two possibilities for the 5th point, either A or B

gets it

- A wins

- B wins

Total number of possible outcomes = 4 (case 1+ case 2)

Number of outcomes where A wins = 2+1 [2 in case 1+1 in case 2] =3

Probability =34


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