Question

One card is drawn at random from a deck of 52 cards. The first card is not replaced, and a second card is drawn. (Enter your probabilities as fractions.)
Required:
a. Find the probability that both cards are clubs.
b. Find the probability that the first card is a spade and the second is a club.

Answer 1

Answer:

We have a 52 card deck:

a. Find the probability that both cards are clubs.

The probability of drawing a club will be equal to the quotient between the number of clubs in the deck divided by the total number of cards in the deck.

We initially have 13 clubs and 52 cards, then the probability of drawing a club in the first draw is:

p1 = 13/52.

Now the probability of drawing a club in the second draw will be:

p2 = 12/51

Where each number is decreased by one because we already drew a card, and that card was a club.

Then the probability of both events happening will be equal to the product of the individual probabilities:

P = p1*p2 = (13/52)*( 12/51) = 0.059

b. Find the probability that the first card is a spade and the second is a club.

Same as before, the probability of first drawing a spade is:

p1 = 13/52

And the probability of drawing a club in the second draw will be:

p2 = 13/51

This case differs from the prior one because for the second draw we have 13 clubs in the deck, and as we already drew one card (that was not a club) the total number of cards in the deck is 51.

Now the joint probability will be:

P = p1*p2 = (13/52)*(13/51) = 0.064