5. Problem 4. In a certain card game, each card has a point value. • Numbered cards in the range 2 to 9 are worth five points each. • The card numbered 10 and the face cards (jack, queen, king) are worth ten points each. • Aces are worth fifteen points each. (a) Suppose that you thoroughly shuffle a 52card deck. What is the expected total point value of the three cards on the top of the deck after the shuffle? (b) Suppose that you throw out all the red cards and shuffle the remaining 26card, allblack deck. Now what is the expected total point value of the top three cards? (Note that drawing three aces, for example, is now impossible!)
5. Problem 4. In a certain card game, each card has a point value. • Numbered cards in the range 2 to 9 are worth five points each. • The card numbered 10 and the face cards (jack, queen, king) are worth ten points each. • Aces are worth fifteen points each. (a) Suppose that you thoroughly shuffle a 52card deck. What is the expected total point value of the three cards on the top of the deck after the shuffle? (b) Suppose that you throw out all the red cards and shuffle the remaining 26card, allblack deck. Now what is the expected total point value of the top three cards? (Note that drawing three aces, for example, is now impossible!)
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:5. Problem 4. In a certain card game, each card has a point value.
• Numbered cards in the range 2 to 9 are worth five points each.
• The card numbered 10 and the face cards (jack, queen, king) are worth ten points each.
• Aces are worth fifteen points each.
(a) Suppose that you thoroughly shuffle a 52card deck. What is the expected total point value of
the three cards on the top of the deck after the shuffle?
(b) Suppose that you throw out all the red cards and shuffle the remaining 26card, allblack deck.
Now what is the expected total point value of the top three cards? (Note that drawing three
aces, for example, is now impossible!)
Expert Solution
Step 1
Given that,
The card has the following point values.
- Numbered cards in the range of 2 to 9 are worth five points each
- The card number 10 and face cards are worth ten points each
- Aces are worth fifteen points each
The probability is the ratio of number of favorable outcomes of the events to the total number of outcomes
The formula for the expected value is as follows,
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