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20 Find the probability of drawing 2 Queens and 3 Kings Hint how many 5-cand hands have 2 Queens and 3 Kinge? (o supues

20 Find the probability of drawing 2 Queens and 3 Kings Hint how many 5-cand hands have 2 Queens and 3 Kinge? (o supues

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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**Problem Statement:** 20. Find the probability of drawing 2 Queens and 3 Kings. *Hint: how many 5-card hands have 2 Queens and 3 Kings?* (There are 4 Queens and 4 Kings in a deck of cards.) **Solution Approach:** 1. **Understand the Problem:** - A standard deck of cards has 52 cards. - You need to find the probability of drawing a 5-card hand with exactly 2 Queens and 3 Kings from this deck. 2. **Calculate Combinations:** - Determine the number of ways to choose 2 Queens out of 4. - Determine the number of ways to choose 3 Kings out of 4. 3. **Total Possible 5-Card Hands:** - Calculate the total number of possible 5-card combinations from a 52-card deck. 4. **Use the Formula for Probability:** - Probability = (Number of favorable outcomes) / (Total number of possible outcomes) This probability calculation involves combinatorial mathematics, specifically the use of binomial coefficients to identify combinations.
Transcribed Image Text:**Problem Statement:** 20. Find the probability of drawing 2 Queens and 3 Kings. *Hint: how many 5-card hands have 2 Queens and 3 Kings?* (There are 4 Queens and 4 Kings in a deck of cards.) **Solution Approach:** 1. **Understand the Problem:** - A standard deck of cards has 52 cards. - You need to find the probability of drawing a 5-card hand with exactly 2 Queens and 3 Kings from this deck. 2. **Calculate Combinations:** - Determine the number of ways to choose 2 Queens out of 4. - Determine the number of ways to choose 3 Kings out of 4. 3. **Total Possible 5-Card Hands:** - Calculate the total number of possible 5-card combinations from a 52-card deck. 4. **Use the Formula for Probability:** - Probability = (Number of favorable outcomes) / (Total number of possible outcomes) This probability calculation involves combinatorial mathematics, specifically the use of binomial coefficients to identify combinations.
Expert Solution
Step 1

 

Obtain the probability of drawing 2 queens and 3 kings.

 

The probability of drawing 2 queens and 3 kings is obtained below as follows:

 

From the information, it is clear that there is a total of 52 cards in a deck of cards among which there are four kinds of suits each with the 13 cards of (spade, clubs, heart, diamond).

 

That is, there are two red suits (hearts and diamonds) and the two black suits(spade, clubs).

 

The total number of cards in deck=52.

The total number of queen cards in 4 suits=4

The total number of king cards in 4 suits=4

 

Let E denote the event that the probability of drawing 2 queens and 3 kings.

 

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