Multiple choice problem. You pay $5 to play a game which consists of shuffling a

Question

Multiple choice problem. You pay $5 to play a game which consists of shuffling a deck of cards then drawing a card at random. If one of the 10, J, Q, K, or A appear you fail to win anything. However, you win $1 for each draw in which one of the mentioned cards do not appear. The game ends the first time one of those cards are drawn. Your expected winnings in this game is: (a) E(X-1) where X ~ Bin (52, 5/13) (b) E(5-X) where X ~ Geom (5/13) (c) E(X-6) where X ~ Geom (5/13) (d) E(X-5) where X ~ NegBin (5, 5/13) (e) E(1-X) where X ~ NegBin (1, 5/13) (f) E(4-X) where X ~ Bin (5, 5/13)

Explanation / Answer

X is the amount we win at the end of the game.

But we paid 5 at the beginning.

If E[X] is the expected amount won by us.

Then E[X-5] is the total profit for us. Hence Ans is Option d)

And it follows a NegBin(5,5/13)

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.