Question

An urn contains 10 white and 5 black balls. The balls are removed without replacement one at a time. What is the probability that 5 white balls are removed before 3 black balls are?

Answer 1

Step - 1: Finding probability of individual events

Given an urn contains 10 black and 5 white balls.

So, total number of balls = 10+5 = 15

Let A be the event of first ball being black and B denote the event of second ball being black

P(A) =

Total number of balls

Number of black balls

​

⇒ P(A) =

15

10

​

=

3

2

​

P(B) =

Total number of remaining balls

Number of remaining black balls

​

(as ball is not replaced)

⇒ P(B) =

14

9

​

Step - 2: Finding total probability

Probability that both the balls drawn are black, P = P(A) × P(B)

⇒ P =

3

2

​

×

14

9

​

⇒ P =

7

3

​

Hence, the probability that both the balls drawn are black is

7

3

​