Question

In a standard deck cards there are 13 spades , 13clubs, 13 hearts and 13 diamonds the spades and the clubs are black and the hearts and the diamonds are red. If two cards are chosen at random one at a time and replaced after each pick. What is the probability that black card is chosen first and heart is chosen second?

Answer 1

Black card 26 out of 52 or 1/2 or 50% chance.  As far as it being a heart the odds go to 13 out of 52 or 25%.

Answer 2

The required probability is 1/8.

Step-by-step explanation:

In a standard deck cards there are 13 spades , 13 clubs, 13 hearts and 13 diamonds.

Total cards =
`13+13+13+13=52`

The spades and the clubs are black and the hearts and the diamonds are red.

Means 26 cards are red and 26 cards are black.

Now, 1 heart card can be drawn from a pack of 13 heart cards in 13C1 ways or 13C1=13

And 1 card can be drawn from a pack of 52 cards in 52C1 ways or 52C1=52

So, the probability of drawing a heart card from 52 cards is
`13/52=1/4`

Similarly, 1 black card can be drawn from a pack of 26 black cards in 26C1 ways or 26C1=26

And 1 card can be drawn from 52 cards in 52C1 ways or 52C1=52

Therefore, the probability of drawing a black card from a pack of 52 cards is

`26/52=1/2`

Hence, the probability (combined) is =
`1/4*1/2=1/8`