Question

A square dart board is divided into four equal squares as shown in the figure given below. If a dart hits square APOS, a player wins ₹ 100. If a dart hits square BPOQ, a player loses ₹ 50. If a dart hits square OQCR, a player loses ₹ 100 and if it hits square ORDS, the player will win ₹ 25. A player takes a turn and hits the dart board. What is the probability that

1. the player loses money?
2. the player wins 100?

Answer 1

Given:

The square dart board is divided into 4 equal squares: APOS, BPOQ, OQCR and ORDS.

Total number of equal outcomes = 4

(i) Probability that the player loses money:

Player loses money if the dart hits square BPOQ (loses ₹ 50) or square OQCR (loses ₹ 100).

Number of favorable outcomes = 2

P(losing money) = `"Number of favorable outcomes"/"Total number of outcomes"`

P(losing money) = `2/4 = 1/2`

(ii) Probability that the player wins ₹ 100:

Player wins ₹ 100 only if the dart hits square APOS.

Number of favorable outcomes = 1

P(winning ₹ 100) = `1/4`