Question

A bag contains 6 red balls and 5 black balls . Two balls are picked , one after the other . Find the probability that :

i. Both are black
ii. The first is black
iii. Both are of the same colour
Given that :
a. it is without replacement
b. it is with replacement

Answer 1

There are:

• 6 red balls - R
• 5 black balls - B
• Total number = 11 balls

A. Without replacement

i. Two blacks

• P(BB) = 5/11*4/10 = 2/11

ii. The first is black

• P(B) = 5/11

or, alternatively

• P(BR or BB) = 5/11*6/10 + 2/11 = 3/11 + 2/11 = 5/11

iii. Both are of same colour

• P(BB or RR) = 2/11 + 6/11*5/10 = 2/11 + 3/11 = 5/11

B. With replacement

i. Two blacks

• P(BB) = 5/11*5/11 = 25/121

ii. The first is black

• P(B) = 5/11

or alternatively

• P(BR or BB) = 5/11*6/11 + 25/121 = 30/121 + 25/121 = 55/121 = 5/11

iii. Both are of same colour

• P(BB or RR) = 5/11*5/11 + 6/11*6/11 = 25/121 + 36/121 = 61/121