Question

You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.

Answer 1

`(25)/(102)`

Explanation:

"AND" means Multiplication, and

"OR" means Addition (in probability)

We want Both cards to be black, that means 1st card black "AND" 2nd card black. So we find individual probabilities and MULTIPLY.

There are 26 black cards from 52 total cards in a normal deck.

P(1st card black) = 26/52 = 1/2

Now, since we HAVEN'T REPLACED, there are now 25 black cards out of 51 total cards. So

P(2nd card black) = 25/51

Now we multiply:

P(both black) =
`(1)/(2)*(25)/(51)=(25)/(102)`