A committee of three is to be chosen from a group of four women and three men. What is the probability that the committee will consist of one man and two women?

Question

BlackTom AI · Accepted Answer

Let me restate the problem in my own words to ensure understanding: we have a pool of 4 women and 3 men, and we want the probability that a randomly formed committee of 3 people contains exactly 1 man and 2 women.

First, determine the total number of possible 3-person committees from the 7 people. This is a combination problem: C(7,3) = 35 total committees.

Next, count the favorable committees that have exactly 1 man and 2 women. To form such a committee, we must choose:
- 1 man from the 3 available men: C(3,1) = 3 ways
- 2 women from the 4 available women: C(4,2) = 6 ways

Multiply these because the choices are independent: 3 × 6 = 18 favorable committees.

Therefore, the probability is the number of favorable outcomes over the total outcomes: 18/35.

If you compare to the provided answer label (such as d. 18/35), this matches the computed probability. Note: since the actual list of answer options was not included in the data here, I’m focusing on the calculation that yields the 18/35 result and how it aligns with the given solution format.

MUF0092 Mathematics Unit 2-SEM 1-2025 9.8 Entire Study Area 2 Revision Questions

A committee of three is to be chosen from a group of four women and three men. What is the probability that the committee will consist of one man and two women?

View Explanation

Log in for full answers

Similar Questions

There are 52 balls in a box. 13 are red, 20 are white, and the other are blue. You pick up 5 balls without replacement. What is the probability that you pick up at least 1 red balls?

Question at position 11 If P(A) = 0.24 and P( B )=0.52 and A and B are independent, what is P(A or B)?0.12480.6352Approximately 00.760.28

Question at position 6 In a certain town, 20% of the households have an electric vehicle, 40% have a hybrid vehicle, and 10% have both. What percent of households have neither an electric nor a hybrid vehicle?0%30%10%70%50%

You have a trick coin that lands on Head 70% of the time. You flip this coin twice. What is the probability you have 1 head and 1 tail? Give the answer as a decimal ( .0.58 for a probability of 58%)

位置1的问题 Suppose X is a random variable representing rolling a six-sided dice. Assume the dice is fair, so there is an equal probability of rolling any number 1 through 6. What is the following probability? P(2≤X≤5) 13231256清除选择

位置1的问题 Suppose X is a random variable representing rolling a six-sided dice. Assume the dice is fair, so there is an equal probability of rolling any number 1 through 6. What is the following probability? P(2≤X≤5) 13562312清除选择

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler