Question

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. find the probability that both cards are black. express your answer as a simplified fraction.

Answer 1

Answer:

$\frac{25}{102}$.

Step-by-step explanation:

Total number of cards in a deck = 52

number of black cards in a deck = 26

Find the probability that both cards are black (without replacement).

Therefore, both events are dependent.

The probability of first card is black = $P_{1}=\frac{26}{52}$

the probability of second card is black = $P_{2}=\frac{25}{51}$

$P=\frac{26}{52}$ × $=\frac{25}{51}$

   = $\frac{1}{2}$ × $\frac{25}{51}$

   = $\frac{25}{102}$

The probability that both cards are black is $\frac{25}{102}$.