Question

Read the following passage:

"Eight Ball" is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15. The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random.

Based on the above information, answer the following questions:

1. What is the probability that the drawn ball bears number 8?
2. What is the probability that the drawn ball bears an even number?
   OR
   What is the probability that the drawn ball bears a number, which is a multiple of 3?
3. What is the probability that the drawn ball is a solid coloured and bears an even number?

Answer 1

i. Probability of no. 8 = `1/"Total no. of balls"`

= `1/15`

ii. Even number balls are 2, 4, 6, 8, 10, 12, 14

Total number of even number balls = 7

∴ Probability of an even number ball

= `"No. of even balls"/"Total no. of balls"`

= `7/15`

OR

Multiples of 3 between 1 to 15 are 3, 6, 9, 12, 15

Total number of balls which is multiple of 3 = 5

∴ Probability of multiple of 3 ball

= `"No. of multiple of 3 balls"/"Total no. of balls"`

= `5/15`

= `1/3`

iii. Solid coloured and even number balls are 2, 4, 6, 8

∴ Required probability

= `"No. of favourable outcomes"/"Total no. of outcomes"`

= `4/15`