Question

Question #34319

Answer 1

`P(A,J,Q,K) = 16/52 = 4/13`

Explanation:

"OR" implies that either of the conditions is fine.
Obviously in cards we could not have a card being an Ace AND a King, but it could be an Ace AND a heart.

In a deck there is an ace, and 3 face cards (J,Q,K) in each of the four suits. [This could already give us the answer as `4/13`]

Considering the whole deck - there are `4xx4 = 16` cards which we want.

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

`P(A,J,Q,K) = 16/52 = 4/13`

Answer 2

`4/13`

Explanation:

Probability is all about counting. Higher up the educational scale the counting can get quite complicated but it is still about counting.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Assumption: The joker is excluded")`

`color(brown)("The count of what we are after")`
The cards we may select are: Ace, King, Queen and Jack

This is 4 cards

There are 4 different types of card sets these are:

Clubs, Spades, Diamonds, Hearts.

Each of these have the ace, king etc

So the target potential selection count is

`4xx4=16`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("The count of the whole -all of them")`

A pack of cards (excluding the joker) is 52

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("The probability of selecting our target cards")`

So the count of cards we wish to aim for is `16/52`

There is that fraction again!

`=4/13`