 Hi friends, I am Purva and today we will discuss the following question. Two cards are drawn at random and without replacement from a pack of 52 plain cards. Find the probability that both the cards are black. Let E and F be two events. Then the conditional probability of an event F given the occurrence of event E is given by probability of F given E is equal to probability of E intersection F upon probability of E and here we have probability of E is not equal to 0. Now we can write this as probability of E intersection F is equal to probability of E into probability of F given E and and here probability of E is not equal to 0. This is the multiplication rule. So this is the key idea behind our question. Let us begin with the solution now. Now let A and B denote the events of drawing black card in first draw and second draw respectively. Then we have to find probability of A intersection B that is the probability that both the cards are black. Now probability of A that is probability of drawing black card in first draw is equal to 26 upon 52 because total number of playing cards are 52 and out of 52 cards half of them are black cards that is 26 of them are black cards. So the probability of drawing a black card out of 52 playing cards will be 26 upon 52. Now we are given that second card is drawn without replacement. Thus we have to find probability of B given that A has occurred that is we have to find probability of B given A. Now the total number of playing cards are 52 out of which we have drawn one black card, so we are left with 51 cards. Now we have to find the probability of drawing the black card from these 51 cards. Since we have already drawn one black card, so the number of black cards is now reduced to 25 from 26. So the probability of drawing the second black card from the left out 51 cards is 25 upon 51. That is probability of B given A is equal to 25 upon 51. Now by multiplication rule of probability we have probability of A intersection B is equal to probability of A into probability of B given A and this is equal to 26 upon 52 into 25 upon 51 and this is equal to 25 upon 102. So we have got probability of A intersection B is equal to 25 upon 102. Thus we have got our answer as 25 upon 102. Hope you have understood the solution. Bye and take care.