Question

In a gambling game a person draws a single card from an ordinary 52-card playing deck. A person is paid $17 for drawing a jack or a queen and $5 for drawing a king or an ace. A person who draws any other card pays $2. If a person plays this game, what is the expected gain

Answer 1

`E.G=\$2`

Explanation:

Sample size 52 card

Pay for J or Q
`=\$17`

Pay for King or Ace
`=\$5`

Pay for others
`=-\$2`

Therefore

Probability of drawing J or Q

`P(J&Q)=(8)/(52)`

Probability or drawing King or Ace

`P(K or A)=(8)/(52)`

Probability or drawing Other cards

`P(O)=(36)/(52)`

Therefore

Expected Gain is mathematically given as

`E.G=\sum_xP(x)`

`E.G=17*(8)/(52)+5*(8)/(52)+(-2)*(36)/(52)`

`E.G=\$2`