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

Answer:

$E.G=\ 2$

Step-by-step 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

$P(J&Q)=\frac{8}{52}$

Probability or drawing King or Ace

$P(K or A)=\frac{8}{52}$

Probability or drawing Other cards

$P(O)=\frac{36}{52}$

Therefore

Expected Gain is mathematically given as

$E.G=\sum_xP(x)$

$E.G=17*\frac{8}{52}+5*\frac{8}{52}+(-2)*\frac{36}{52}$

$E.G=\ 2$