Question

Conditional probability:

Two cards are drawn without replacement from a well-shuffled pack of 52 playing cards.

a. what is the probability that the first card drawn is a heart?

b. what is the probability that the second card drawn is a heart given that the first card drawn was not a heart?

c. what is the probability that the second card drawn is a heart given that the first card drawn was a heart?

Answer 1

a. 1/4

b. 13/51

c. 12/51

Explanation:

Note:
The formula to find probability is:

P(A) = n(A) / n(S)

where:

• P(A) is the probability of event A occurring.
• n(A) is the number of favorable outcomes for event A.
• n(S) is the total number of possible outcomes.

For question:

a.

There are 13 hearts in a standard deck of 52 cards, so the probability of drawing a heart is 13/52.

The probability that the first card drawn is a heart is 13/52 = 1/4.

b.

Since the first card was not a heart, there are 13 hearts left in the deck. There are also 51 cards left in the deck overall, so the probability of drawing a heart is 13/51.

The probability that the second card drawn is a heart given that the first card drawn was not a heart is 13/51.

c.

Since the first card was a heart, there are 12 hearts left in the deck. There are also 51 cards left in the deck overall, so the probability of drawing a heart is 12/51.

The probability that the second card drawn is a heart given that the first card drawn was a heart is 12/51.