Question

A​ 5-card hand is dealt from a standard​ 52-card deck. If the​ 5-card hand contains at least one

king​,

you win

​$11;

​otherwise, you lose

​$3.

What is the expected value of the​ game?

The expected value of the game is

______

dollars.

​(Type an integer or a decimal rounded to two decimal​ places.)

Answer 1

The probability that the 5 card hand contains at least one king is computed here as:
= 1 - Probability that the 5 card dont contain any king

= 1 - (Number of ways to select 5 cards from 48 non king cards / Total ways to select 5 cards from 52 cards )

The expected value of the game here is computed as:
= Probability of winning * Winning amount - (1 - Prob. of losing)*Losing amount

= 0.3412*11 - (1 - 0.3412)*3 = 1.7768

Therefore $1.78 is the required expected value of the game here.