You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Card rule: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. ***The image is the example*** Questions: If there are n = 4 cards in the deck, determine the expected value of your final score. Show your calculations.

You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Card rule: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. The image is the example Questions: If there are n = 4 cards in the deck, determine the expected value of your final score. Show your calculations.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time.

Card rule: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over.

***The image is the example***

Questions:

If there are n = 4 cards in the deck, determine the expected value of your final score. Show your calculations.

For example, if n = 3, then there are six possible scenarios, each of them equally likely to occur. The
cards placed on the table are marked in bold.
First Card
Second Card Third Card
Cards on Table Points
1, 2, 3
1, 3
1
3
1
2
1
3
2
1
2
1
2, 3
2
3
1
3
1
3
3
1
Thus, if there are n =
probability
3 cards in the deck, then you score 1 point with probability , 2 points w
final
and the maximum 3 points with probability . And so, the expected value of
your
Score is 1 X
+2 x+3 x =
10
||
1.666.

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