60% of math major are women 15 were random and what probability that 5 are women.
To find the probability that 5 out of 15 randomly chosen math majors are women, we can use the concept of probability and combinations.
Given that 60% of math majors are women, it implies that 40% are men. We need to calculate the probability of choosing 5 women from a group of 15 math majors.
First, we need to determine the number of ways to choose 5 women from a group of 15 math majors. This can be calculated using combinations. The formula for combinations is:
nCr = n! / (r! * (n - r)!)
where n is the total number of objects, and r is the number of objects chosen.
In this case, we want to calculate 15C5, which represents choosing 5 math majors from a group of 15. Using the combination formula:
15C5 = 15! / (5! * (15 - 5)!)
= 15! / (5! * 10!)
Now, the numerator can be simplified further:
15! = 15 * 14 * 13 * 12 * 11 * 10!
Substituting this back into the equation:
15C5 = (15 * 14 * 13 * 12 * 11 * 10!) / (5! * 10!)
The 10! terms cancel out:
15C5 = (15 * 14 * 13 * 12 * 11) / 5!
5! = 5 * 4 * 3 * 2 * 1
15C5 = (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
Now, we can calculate the probability. The probability of choosing 5 women would be the number of ways to choose 5 women divided by the total number of combinations:
P(5 women) = 15C5 / 15C15
P(5 women) = (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
Simplifying further:
P(5 women) = 3003 / 3003
P(5 women) = 1
Therefore, the probability that 5 randomly chosen math majors out of a group of 15 are women is 1, or 100%.