Answer:
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: [tex]\dfrac{8}{52}[/tex]
$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: [tex]\dfrac{8}{52}[/tex]
Now the remaining cards are: 52-8-8=36
So probability of getting other card is: [tex]\dfrac{36}{52}[/tex]
The expected probability is:
[tex]E(Y)=\sum P(x_i)\times x_i[/tex]
[tex]E(Y)=18\times\dfrac{8}{52}+7\times\dfrac{8}{52}-4\times\dfrac{36}{52}[/tex]
[tex]E(Y)=\dfrac{36}{13}+\dfrac{14}{13}-\dfrac{36}{13}[/tex]
[tex]E(Y)=\dfrac{14}{13}\approx\$1.077[/tex]
Hence, the expected gain is $1.077
