Find the expectation of a game

Question

A gamble draws a card from an ordinary deck of cards. If it is a black card, she wins $2. If it is a red card between or including 3 and 7, she wins $10. If it is a red face card, she wins $25, and if it is a black jack, she wins an additional $100. If it is any other card, she wins nothing. Find the expectation of the game.

Answer 1

Prob(Black card)*$2 + Prob (red card that is 3,4,5,6,7)*$10 + Prob(red face card)*$25 + prob( black jack)*$100 =

 

 

 26/52 * 2 +  10/52*10 + 6/52 * 25 + 2/52*100 =

 

1/2*2 + 5/26*10  + 3/26*25 + 1/26*100 =

 

1 + 50/26 + 75/26 + 100/26 =

 

(26 + 50+ 75 + 100)/26 =

 

251/26 =

 

$9.66