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

Total number of cards = 52
Number of black cards = 26
Let E and F denote respectively events that first and second balls drawn are black
$therefore space space space space straight P left parenthesis straight E right parenthesis space equals space straight P left parenthesis black space ball space in space first space draw right parenthesis space equals space 26 over 52$
$straight P left parenthesis straight F vertical line straight E right parenthesis space equals space 25 over 51$
Required probability = P(E) P(F|E)
$equals space 26 over 52 cross times 25 over 51 space equals 25 over 102$

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Probability

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.

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