Question

A bag contains 3 black and 4 red balls . Two balls are drawn at random one at a time without replacement . The probability that the first ball drawn is black if the second ball is known to be red

Answer 1

Red =3

Black=7

Total=10

Let,P(A)= Probability that first is red.

P(B)=Probability that second is red:

Second is red ,There are 2 possible ways.

Either First is red and second is red.

Or First is black and Second is red.

So,

P(B)= (3c1/10 ×2c1/9 )+(7c1/10 ×3c1/9)

6/90 + 21/90

27/90

=0.3

Probability that first is red, given second is red.

P(A/B)

=P(A intersection B)/P(B).

=Probability that both first and second are red/Probability that second is red.

=(3c1/10 × 2c1/9)÷0.3

=6/90 ÷ 3/10

=6/90 × 10/3

=6/27

=2/9.

=0.2222

Hope it helps :)