Question

Find the indicated probability. 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

There are total 52 cards out of which there are 26 black cards and there are 26 red cards

Probability of picking a first black card = 26/52 = 1/2

Probability of picking a second black card = 25/51 (since one card is already picked, we are left with 51 cards out of which 25 cards are black

We have been asked to find the probability of picking two cards that are black.

So the probability that both cards picked are black = (1/2) * (25/51)

= 25/102 in the simplest fraction form

= 0.245098 in decimal form

We have multiplied the two probabilities since the event is comprising of picking both black cards