Two balls are drawn in succession out of a box containing 2

Two balls are drawn in succession out of a box containing 2 red and 5 white balls. The balls are drawn without replacement. What is the probability that both balls drawn are red?

Solution

Two balls are drawn independently out of a box containing 2 red and 5 black balls.

Let A be the event that the first ball drawn is red and B be the event that the second ball drawn is red.

then, P(A)=2/7

the required probability is given by,

P(AB)=P(A)*P(B given A)

Now, P(B given A)=P(second ball drawn is red given that the first ball drawn is red)=1/6

[since the drwing was under without replacement scheme]

therefore,P(AB)=(2/7)*(1/6)=1/21