Question

Two cards are drawn from a standard deck without replacement. What is the probability that the first card is a club and the second card is red? (

Answer 1

Answer:

Probability to draw a club and second card is red without replacement will be $\frac{13}{102}$ or 12.75%

Step-by-step explanation:

A standard deck of cards contains number of cards = 52

And a standard deck contains number of club = 13

Now the probability of first card to be a club will be

$P_{1}=\frac{\text{Number of club in a deck}}{\text{Total number of cards}}$

    = $\frac{13}{52}=\frac{1}{4}$

Now this card is separated from the deck.

Therefore, number of remaining cards = 52 - 1 = 51

Second card has been drawn from the deck without replacement.

Since number of red cards in the deck = 13 + 13 = 26

Probability of the second card drawn = $\frac{\text{Number of red cards}}{\text{Number of remaining cards}}$

$P_{2}=\frac{26}{51}$

Now probability that the first card is a club and the second card is red = $P_{1}\times P_{2}=\frac{1}{4}\times \frac{26}{51}$

= $\frac{13}{102}$

Or $\frac{13}{102}\times 100=12.75%$%

Therefore, probability to draw a club and second card is red without replacement will be $\frac{13}{102}$ or 12.75%