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1. Suppose we are dealt 7 cards from a well-shuffled standard deck. (You may leave terms like (2) in your answer.) (a) What is the probability of 3 pairs? (b) What is the probability of 4 of one kind and 3 of another? (c) What is the probability of 4 aces and 3 of another kind? (d) What is the probability of all seven cards being in the same suit? (e) Let N be the number of aces that you are dealt. What is P{N = k} for k = 0, 1, 2, 3, 4. (You could work this out for each value of k, which is fine. However, you might also be able to figure out how to write your answer as a function of k, which involves a lot less writing.)

1. Suppose we are dealt 7 cards from a well-shuffled standard deck. (You may leave terms like (2) in your answer.) (a) What is the probability of 3 pairs? (b) What is the probability of 4 of one kind and 3 of another? (c) What is the probability of 4 aces and 3 of another kind? (d) What is the probability of all seven cards being in the same suit? (e) Let N be the number of aces that you are dealt. What is P{N = k} for k = 0, 1, 2, 3, 4. (You could work this out for each value of k, which is fine. However, you might also be able to figure out how to write your answer as a function of k, which involves a lot less writing.)

A First Course in Probability (10th Edition)
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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1. Suppose we are dealt 7 cards from a well-shuffled standard deck. (You may leave terms like (2) in your answer.) (a) What is the probability of 3 pairs? (b) What is the probability of 4 of one kind and 3 of another? (c) What is the probability of 4 aces and 3 of another kind? (d) What is the probability of all seven cards being in the same suit? (e) Let N be the number of aces that you are dealt. What is P{N = k} for k = 0, 1, 2, 3, 4. (You could work this out for each value of k, which is fine. However, you might also be able to figure out how to write your answer as a function of k, which involves a lot less writing.)
Transcribed Image Text:1. Suppose we are dealt 7 cards from a well-shuffled standard deck. (You may leave terms like (2) in your answer.) (a) What is the probability of 3 pairs? (b) What is the probability of 4 of one kind and 3 of another? (c) What is the probability of 4 aces and 3 of another kind? (d) What is the probability of all seven cards being in the same suit? (e) Let N be the number of aces that you are dealt. What is P{N = k} for k = 0, 1, 2, 3, 4. (You could work this out for each value of k, which is fine. However, you might also be able to figure out how to write your answer as a function of k, which involves a lot less writing.)
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