1st problem: You have five decks of cards, each with 52 cards. On each deck, you are allowed to draw only 10 cards. Of each set of 10 drawn cards, you set aside the cards in the suit of hearts, then you assemble all of the collected hearts you have drawn from those 50 cards, eliminating any duplicates. You place them 2 through Ace in a horizontal layout. What is the probability of obtaining no hearts? Or 1, 2, etc, up to all 13 hearts?
1st problem: You have five decks of cards, each with 52 cards. On each deck, you are allowed to draw only 10 cards. Of each set of 10 drawn cards, you set aside the cards in the suit of hearts, then you assemble all of the collected hearts you have drawn from those 50 cards, eliminating any duplicates. You place them 2 through Ace in a horizontal layout. What is the probability of obtaining no hearts? Or 1, 2, etc, up to all 13 hearts?
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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Transcribed Image Text:1st problem:
You have five decks of cards, each with 52 cards. On each
deck, you are allowed to draw only 10 cards. Of each set
of 10 drawn cards, you set aside the cards in the suit of
hearts, then you assemble all of the collected hearts you
have drawn from those 50 cards, eliminating any
duplicates.
You place them 2 through Ace in a horizontal layout. What
is the probability of obtaining no hearts? Or 1, 2, etc, up to
all 13 hearts?
2nd problem:
What are the probabilities of being able to string together 4
or more sequential hearts in your layout? What about 5?
6, etc, - all the way up to 13.
3rd problem:
So, now, with these sequential-based probabilities in mind,
imagine that the player is betting $1 for this chance to
string together sequential hearts from these 50 cards from
five decks. Based on those odds, what would be the
appropriate payout for achieving a string of 4 sequential
hearts, 5, and so on, keeping in mind that there is also the
potential to create more than one string of hearts in
sequence of 4 or more within the range of 13 places. 3-6
and 9-K, for example.
The goal in calculating these paybacks is for the game to
pay back 98% of the player's bet over an indefinite amount
of time.
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