Question

Consider drawing two cards, without replacement, from a standard deck of 52 cards. That means we are drawing the first card, leaving it out, and then drawing the second card.what is the probability that both cards selected for black?

Answer 1

Given:

Two cards are drawn from a standard deck of 52 cards without replacement.

To find:

The probability that both cards selected for black.

Solution:

We know that,

Total number of cards = 52

Total number of red cards = 26

Total number of black cards = 26

$\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

Probability of selecting first black card is

$\text{Probability}=\dfrac{26}{52}$

$\text{Probability}=\dfrac{1}{2}$

Number of remaining total cards = 52-1 = 51

Number of remaining black cards = 26-1 = 25

Probability of selecting second black card is

$\text{Probability}=\dfrac{25}{51}$

So, the probability that both cards selected for black is

$\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}$

$\text{Probability}=\dfrac{25}{102}$

Therefore, the required probability is $\dfrac{25}{102}$.