Card Probabilities?

Question

I'm trying to explain this to a friend. Can you help me?

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

1. Probability 1st card drawn is a heart and the second card is also a heart?

2. Probability 1st card is a Jack and 2nd card is a five?

Answer 1

PROBLEM 1:

First card has a 13/52 chance (or 1/4) of being a heart.
Second card has a 12/51 chance (or 4/17) of being a heart.

So the combined probability of drawing two hearts is 1/4 x 4/17 = 1/17 ≈ 5.882%

PROBLEM 2:

First card has a 4/52 chance (or 1/13) of being a jack
Second card has a 4/51 chance of being a five.

The combined probability is:
1/13 x 4/51 ≈ 0.603%

Answer 2

1. There are 52/4=13 hearts in a standard deck. The probability the 1st card drawn is a heart is 13/52. For the second card, now there are 12 hears in a deck of 51. Thus, the probability is as follows:

13/52 x 12/51 = 0.0588

2. There are 4 Jacks and 4 fives is a standard deck of 52. Similar to above, the probability will be:

4/52 x 4/51 = 0.0060

Answer 3

1. P(first card is a heart and second card is also a heart)
= (13/52)*(12/51)
= 1/17
= 0.0588

2. P(first a jack abd second a five)
= (4/52)*(4/51)
= 4/663
= 0.0060

Answer 4

1) the probability the first is a heart is 13/52, the prob the second is also a heart is 12/51, their product is the total prob, 156/2652.

2) p(jack)=4/52, p(5)=4/51, p(total)=16/2652.