(Type a fraction. Simpliry 10. A city council consists of eight Democrats and eight Republicans. If a committee of five people is selected, find the probability of selecting three Democrats and two Republicans.

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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 10 

**Probability and Combinatorics Practice Problems**

7. **Selection from a Group:**
   A group consists of five men and seven women. Four people are selected to attend a conference.

   a. In how many ways can four people be selected from this group of twelve?  
   b. In how many ways can four women be selected from the seven women?  
   c. Find the probability that the selected group will consist of all women.  

   - a. The number of ways to select four people from the group of twelve is _____.  
   - b. The number of ways to select four women from the group of seven women is _____.  
   - c. The probability is ______ (Type an integer or a simplified fraction.)

8. **Lottery Probability:**
   In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 41) and matching the number on the gold ball (1 through 33). If one ticket is purchased, what is the probability of winning the jackpot?

   - The probability of winning the jackpot with one ticket is ______ (Type an integer or a simplified fraction.)

9. **Defective Transistors:**
   A box contains 11 transistors, 5 of which are defective. If 5 are selected at random, find the probability of the statements below.

   a. The probability is ____.  
   b. The probability is ____ (Type a fraction. Simplify your answer.)

10. **City Council Selection:**
    A city council consists of eight Democrats and eight Republicans. If a committee of five people is selected, find the probability of selecting three Democrats and two Republicans.

    - (Type a fraction. Simplify your answer.)

11. **Deck of Cards:**
    A hand consists of 5 cards from a well-shuffled deck of 52 cards.

    a. Find the total number of possible 5-card poker hands.  
    b. A spade flush is a 5-card hand consisting of all spade cards. Find the number of possible spade flushes.  
    c. Find the probability of being dealt a spade flush.

    - a. There are a total of _____ poker hands.  
    - b. There are _____ possible spade flushes.  
    - c. The probability is ________ (Round to six decimal places as needed.)

12. **Picture Cards Probability:**
    If you
Transcribed Image Text:**Probability and Combinatorics Practice Problems** 7. **Selection from a Group:** A group consists of five men and seven women. Four people are selected to attend a conference. a. In how many ways can four people be selected from this group of twelve? b. In how many ways can four women be selected from the seven women? c. Find the probability that the selected group will consist of all women. - a. The number of ways to select four people from the group of twelve is _____. - b. The number of ways to select four women from the group of seven women is _____. - c. The probability is ______ (Type an integer or a simplified fraction.) 8. **Lottery Probability:** In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 41) and matching the number on the gold ball (1 through 33). If one ticket is purchased, what is the probability of winning the jackpot? - The probability of winning the jackpot with one ticket is ______ (Type an integer or a simplified fraction.) 9. **Defective Transistors:** A box contains 11 transistors, 5 of which are defective. If 5 are selected at random, find the probability of the statements below. a. The probability is ____. b. The probability is ____ (Type a fraction. Simplify your answer.) 10. **City Council Selection:** A city council consists of eight Democrats and eight Republicans. If a committee of five people is selected, find the probability of selecting three Democrats and two Republicans. - (Type a fraction. Simplify your answer.) 11. **Deck of Cards:** A hand consists of 5 cards from a well-shuffled deck of 52 cards. a. Find the total number of possible 5-card poker hands. b. A spade flush is a 5-card hand consisting of all spade cards. Find the number of possible spade flushes. c. Find the probability of being dealt a spade flush. - a. There are a total of _____ poker hands. - b. There are _____ possible spade flushes. - c. The probability is ________ (Round to six decimal places as needed.) 12. **Picture Cards Probability:** If you
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