Question

In a gambling game a person draws a single card from an ordinary 52-card playing deck. A person is paid $18 for drawing a jack or a queen and $7 for drawing a king or an ace. A person who draws any other card pays $4. If a person plays this game, what is the expected gain?

Answer 1

The expected gain is $1.077

Explanation:

Consider the provided information.

A person is paid $18 for drawing a jack or a queen.

There are 4 jack and 4 queen in a deck of card.

So probability of getting a jack or a queen is:
`(8)/(52)`

$7 for drawing a king or an ace.

There are 4 king and 4 ace in a deck of card.

So probability of getting a king or a ace is:
`(8)/(52)`

Now the remaining cards are: 52-8-8=36

So probability of getting other card is:
`(36)/(52)`

The expected probability is:

`E(Y)=\sum P(x_i)* x_i`

`E(Y)=18*(8)/(52)+7*(8)/(52)-4*(36)/(52)`

`E(Y)=(36)/(13)+(14)/(13)-(36)/(13)`

`E(Y)=(14)/(13)\approx\$1.077`

Hence, the expected gain is $1.077