The sale force of a business consist of 10 men and 10 women A production unit of 6 people is set up at random what is the probability that it will consist of 4 men and 2 women
To calculate the probability of the production unit consisting of 4 men and 2 women, we need to determine the total number of possible combinations and the number of favorable combinations.
Total number of possible combinations:
In this case, we are selecting a group of 6 people from a total of 20 (10 men and 10 women). The total number of possible combinations can be calculated using the formula for combinations:
nCr = n! / ((n-r)! * r!)
where n represents the total number of options and r represents the number of selections.
In our case, we have:
n = 20 (total number of people)
r = 6 (number of people in the production unit)
Therefore, the total number of possible combinations is:
20C6 = 20! / ((20-6)! * 6!) = 38760
Number of favorable combinations (4 men and 2 women):
Now, we need to determine the number of favorable combinations where there are 4 men and 2 women.
First, calculate the number of combinations of selecting 4 men out of the 10 available men (10C4) and the number of combinations of selecting 2 women out of the 10 available women (10C2).
Using the combination formula:
10C4 = 10! / ((10-4)! * 4!) = 210
10C2 = 10! / ((10-2)! * 2!) = 45
Next, multiply these two values to get the number of favorable combinations:
Number of favorable combinations = 210 * 45 = 9450
Probability:
Finally, divide the number of favorable combinations by the total number of possible combinations to get the probability:
Probability = Number of favorable combinations / Total number of possible combinations
Probability = 9450 / 38760 ≈ 0.2437
So, the probability that the production unit will consist of 4 men and 2 women is approximately 0.2437, or 24.37%.