Question

Suppose that you and a friend are playing cards and decide to make a bet. If you draw three face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards without replacement, you win $40. Otherwise, you pay your friend $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

Answer 1

Answer:

Step-by-step explanation:

Expected value of the bet =

P(you make the correct draw) * 40 + P(you do not make the correct draw) * (-10) =

(4/52)(4/51)(4/50) * 40 + (1 - (4/52)(4/51)(4/50)) * (-10) =

(64/132600) * 40 + (1 - 64/132600) *(-10) =

64/3315 + (132536/132600) * (-10) =

64/3315 - (132536/13260) =

64/3315 - 33134/3315 =

-33070/3315 =

-9.97586726998 =

-$9.98, rounded to the nearest cent  

(i.e., the expected value of the bet is a loss of $9.98)