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?

The expected gain is $1.077

Step-by-step 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:

$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:

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

So probability of getting other card is:  

The expected probability is:

Hence, the expected gain is $1.077

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