+0  
 
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52
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avatar+550 

During a long night of partying, Justin plays a card game where you must pay 10 cents to randomly draw a card from a regular deck of 52 cards. If Justin draws an ace, he wins $2.70. If he draws a heart (but not the ace of hearts), he wins $1.40. If he draws any other card, he wins nothing. What is the mathematical expectation for this game? Express your answer as a decimal in the hundredths place. (Note: In a deck of 52 cards, there are four aces. There are also 13 of each suit including the ace of that suit)

 Mar 11, 2021
 #1
avatar+118069 
+1

My best attempt  :

 

P(ace)  =  4/52  = 1/13

P(heart  but  not the ace of hearts) =  12/52  =  3/13

P(any other  card)  = (52 - 4 - 12) / 52 =    36/52 =  9/13 

 

Expectation  =

 

(1/13)(2.70)  + ( 3/13) (1.40)  - (9/13)(.10)    ≈  .462

 

 

cool cool cool

 Mar 11, 2021
edited by CPhill  Mar 11, 2021
 #2
avatar+550 
+1

thank you!

xxJenny1213xx  Mar 11, 2021

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