Question

A standard deck of 52 cards contains four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards: ace, 2,

3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. Two cards are randomly drawn
without replacement. Calculate the probability of drawing two heart cards.

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, we need to calculate the total number of ways two cards can be drawn from a deck of 52 cards:

There are 13 heart cards in the deck. So, the number of ways we can choose 2 heart cards out of 13 is given by the combination formula:

$$C(13,2) = \frac{13!}{2!(13-2)!} = \frac{13!}{2!11!} = \frac{13*12}{2*1} = 78$$

There are 52 cards in total. So, the number of ways we can choose 2 cards out of 52 is given by the combination formula:

$$C(52,2) = \frac{52!}{2!(52-2)!} = \frac{52!}{2!50!} = \frac{52*51}{2*1} = 1326$$

Therefore, the probability of drawing two heart cards is:

$$ P(\text{two heart cards}) = \frac{C(13,2)}{C(52,2)} = \frac{78}{1326} \approx 0.0588$$

So, the probability of drawing two heart cards from a standard deck of 52 cards is approximately 0.0588 or 5.88%.