Question

Two cards are drawn at random from a standard deck of 52 cards. What is the probability that both cards are aces?

Answer 1

It is not indicated whether the first card is replaced before the second is taken... Let's consider both cases.

`Prob = ("number of desirable outcomes")/("total number of possible outcomes")`

There are 4 aces in a deck of cards which has 52 cards in total.

If the first card is NOT replaced:

P (Ace, Ace) = `4/52 xx 3/51 = 1/221`

(The number of aces remaining is 1 less, and there is 1 less card to choose from.)

If the first card IS replaced , then the probability of drawing an ace stays the same every time a card is chosen:

P (Ace, Ace) = `4/52 xx 4/52 = 1/169`

Note: A probability should be given as a fraction, in the simplest form.
It is always a value from 0 to 1
0 `rArr` (the outcome is impossible)
1 `rArr` (the outcome is guaranteed)