Question

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Answer 1

There are 26 black cards in a deck of cards.

Probability = `(""^26C_1)/(""^52C_1) xx (""^25C_1)/(""^51C_1)`

= `26/52 xx 25/51`

= `50/204`

= `25/102`

Answer 2

Let E₁ be the event that the first drawn card is a back card

⇒ `P(E_1) = 26/52 = 1/2`

Let E₂ be the event when the second drawn card is black without replacement then

`P (E_2|E_2) = 25/51`

Hence the required probability is

`P (E_1 cap E_2) = P (E_1) P(E_2 |E_1)`

`= 26/52 xx 25/51`

`= 25/102`