Question

A playing card is chosen from a standard deck of cards (which contains a total of 52 cards) what is the probability of getting a two. a seven or an ace? a) 3/52 b) 3/13 c) 1/13 d) 1

Answer 1

The probability of drawing either a seven, a two or an ace is `3/13`.

Explanation:

The probability of drawing either an ace, a seven or a two is the same as the probability of drawing an ace plus the probability of a seven plus the probability of a two.

`P=P_(ace)+P_(seven)+P_(two)`

There are four aces in the deck, so the probability must be `4` (the number of "good" possibilities) over `52` (all the possibilities):
`P_(ace)=4/52=1/13`

Since there are `4` of both twos and sevens, we can use the same logic to figure out that the probability is the same for all three:
`P_(seven)=P_(two)=P_(ace)=1/13`

This means we can go back to our original probability:
`P=1/13+1/13+1/13=3/13`

Therefore, the probability of drawing either a seven, a two or an ace is `3 \/ 13`.