Question

Suppose that you and a friend are playing cards and decide to make a bet. If you draw two red cards in succession from a standard deck of 52 cards without replacing the first card, you win $50. Otherwise, you pay your friend $20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

Answer 1

Answer:

E=$19.307

Step-by-step explanation:

Total number of cards = 52

If you win then you will get $50

If you lose then you will give him $20

Therefore the probability

$P(first\ card\ is\ face\ card)=\dfrac{12}{52}$

$P(Second\ card\ is\ face\ card)=\dfrac{11}{51}$

$P(Third\ card\ is\ face\ card)=\dfrac{10}{50}$

Thus the probability for all the three cards are face card

$P=\dfrac{12}{52}\times \dfrac{11}{51}\times \dfrac{10}{50}$

P=0.0099

Thus the probability for all the three cards are not face card

P=1-0.0099=0.9901

P=0.9901

Therefore , expected value

$E=20\times 0.9901-50\times 0.0099$

E=$19.307

Therefore the answer will be $19.307.