A box contains 20 red and 15 black balls. Two balls are drawn from the box one after the other without replacement. What is the probability that both drawn balls are red ?

Explanation

Let E and F denote respectively the events that first and second ball drawn are red. We have to find `P(EcapF) " or " P(EF)`
Now P(E) = P (red ball is first drawn)
`=20/35`
Also given the first ball drawn is red, i.e., event E has occurred, now there are 19 red and 15 black balls left in the box. Therefore, the probability that the second ball drawn is red, given that the ball in the first draw is red, is nothing but the conditional probability of F given that E has occurred
i.e., `P(F|E)=19/34`
By multiplication rule of probability, we have
`P(EcapF)` = P(E) . P(F|E)
`=20/35xx19/34=38/199`