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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.
Solution 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`
Solution 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`
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