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 $\frac{25}{102}$.

Answer 2

The probability that both cards picked without replacement are black is $\frac {25}{102}$

Number of black cards in deck = 26

Total number of cards = 52

Recall :

Probability = (required outcome / Total possible outcomes)

Therefore,

Ist pick :

P(black card) = 26/52

Number of black cards left = 26 - 1 = 25

Total number of cards left = 52 - 1 = 51

2nd pick:

P(black card) = 25 / 51

Therefore, probability that both cards are black is ;

$P(Both \: black) = \frac{26}{52} \times \frac{25}{51} = \frac {25}{102}$

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