Question

To find: The probability of getting same number of men in two groups. Given: A group consists of 6 men and 6 women. Divide into groups 6 in each.

Comparing two groups
ANSWERED
asked 2021-01-30
To find: The probability of getting same number of men in two groups.
Given:
A group consists of 6 men and 6 women. Divide into groups 6 in each.

Answers (1)

2021-01-31
Calculation:
Total number of people \(\displaystyle={6}+{6}={12}\)
All possible ways of dividing 12 people in to two groups with 6 people in each
\(\displaystyle={\frac{{{12}!}}{{{6}!{6}!}}}\)
\(\displaystyle={924}\)
If both groups are having same number of menm then each group consist 3 men and 3 women.
The possible ways of getting 3 men and 3 women in each group is
\(\displaystyle={\frac{{{6}!}}{{{3}!{3}!}}}\times{\frac{{{6}!}}{{{3}!{3}!}}}\)
\(\displaystyle={20}\times{20}\)
\(\displaystyle={400}\)
P(same number of men in each group) \(\displaystyle={\frac{{{400}}}{{{924}}}}\)
\(\displaystyle={0.4329}\)
Hence, the probability \(\displaystyle={0.4329}\)
Answer:
The probability of getting equal number of men in two groups \(\displaystyle={0.4329}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-05-30
There are three women and four men in a group of seven people. If three people are selected from the total of seven, find the following: i)What are the total possible outcomes for this selection? ii)How many ways can two women and one man be selected? iii)What is the probability of selecting two women and one man?
asked 2020-11-09
Consider a group of 8 people. Among them, there is one pair of twins. These 8 people are taken into two different rooms, Room A and Room B, with four people to each room. If all groups of four people are equally likely, find the probability that the twins will be sent into the same room.
asked 2021-06-13
1. Who seems to have more variability in their shoe sizes, men or women?
a) Men
b) Women
c) Neither group show variability
d) Flag this Question
2. In general, why use the estimate of \(n-1\) rather than n in the computation of the standard deviation and variance?
a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation
b) The estimate n-1 is never used to calculate the sample variance and standard deviation
c) \(n-1\) provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population
d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 25.7 & M \\ \hline 25.4 & F \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 26.7 & M \\ \hline 23.8 & F \\ \hline 25.4 & F \\ \hline 25.4 & F \\ \hline 25.7 & M \\ \hline 25.7 & F \\ \hline 23.5 & F \\ \hline 23.1 & F \\ \hline 26 & M \\ \hline 23.5 & F \\ \hline 26.7 & F \\ \hline 26 & M \\ \hline 23.1 & F \\ \hline 25.1 & F \\ \hline 27 & M \\ \hline 25.4 & F \\ \hline 23.5 & F \\ \hline 23.8 & F \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline \end{array}\)
\(\begin{array}{|c|c|}\hline \text{Shoe Size (in cm)} & \text{Gender (M of F)} \\ \hline 27.6 & M \\ \hline 26.9 & F \\ \hline 26 & F \\ \hline 28.4 & M \\ \hline 23.5 & F \\ \hline 27 & F \\ \hline 25.1 & F \\ \hline 28.4 & M \\ \hline 23.1 & F \\ \hline 23.8 & F \\ \hline 26 & F \\ \hline 25.4 & M \\ \hline 23.8 & F \\ \hline 24.8 & M \\ \hline 25.1 & F \\ \hline 24.8 & F \\ \hline 26 & M \\ \hline 25.4 & F \\ \hline 26 & M \\ \hline 27 & M \\ \hline 25.7 & F \\ \hline 27 & M \\ \hline 23.5 & F \\ \hline 29 & F \\ \hline \end{array}\)
asked 2021-02-02
Potential buyers for a new car were randomly divided into two groups. One group was shown the "A" version of an ad for the car, while the other group was shown the "B" version of the ad. All were then tested on their recall of key points made in the ad. The researcher should run a hypothesis test based upon a comparison of means for ?
In another study, a healthcare insurance company took measures of subscribers’ cardiac (heart) health. The people were then provided an app for their phones which provided "nudges" and reminders about heart-healthy behaviors, such as eating more vegetables and less fried or fatty food, taking walks and breaks from sitting too long, and getting enough sleep. After 4 months of having the app, the cardiac health measures were taken again, with the objective of seeing if nudges from the app would result in decreased cardiac risk. The researcher should run a hypothesis test based on a comparison of means for?
...