Question

two cards are drawn at random (without replacement) from a regular deck of 52 cards
a) what is the probability that the first card is a heart and the second is red?

b) what is the probability that the first card is red and the second is a heart?

Answer 1

the probability is that there are 2 out of 52 hearts

the other probability is that there are also 2 out 52 red hearts that you will get

Answer 2

a)
you will have to do this in 2 cases:
1. sequence is red heart, then red
prob = (1/52)(12/51)
2. sequence is non-red heart, then red
prob = (3/52)(13/51)
so prob = (1/52)(12/51) + 3/52)(13/51)
= 12/2652 + 39/2652
= 51/2652
= 1/52

b) again, use the same argument,
it could be ..
-the red-heart, then one of the other 3 hearts, or
- one of the other reds, then one of the hearts.
prob = (1/52)(3/51) + 12/52)(4/51)
= 1/52