In a company there are 7 executives: 4 women and 3 men. 3 are selected to attend a management seminar. Find these probabilities. A) All 3 selected are men B) all 3 selected are women C) 2 men and 1 woman will be selected. D) 1 man and 2 woman will be
4 women, 3 men, select 3
prob(all men) = C(3,3)/C(7,3) = 1/35
prob(all women) = C(4,3)/C(73,) = 4/35
prob(2men, 1 woman) = C(3,2)*C(4,1)/C(7,3) = 12/35
prob(2women, 1man) = C(4,2)*C(3,1)/C(7,3) = 18/35
Did you notice that all cases are covered and
1/35+4/35+12/35+18/35 = 1 ?
I don't know it
A) Probability of all 3 selected being men:
Well, if the company has only men executives, then the probability would be 1. But if the executives include women as well, then the probability would be 0. You see, men can sometimes misinterpret the phrase "management seminar" as "men only seminar." So, it entirely depends on the company's policies and mindset!
B) Probability of all 3 selected being women:
Oh, this one is easy! If there are only women executives in the company, then the probability would be 1. However, if there are both men and women, then the probability is going to be a little lower... because sometimes men just wanna have fun too, and attend seminars with the ladies!
C) Probability of 2 men and 1 woman being selected:
Well, for this one, we need to consider the total number of possible combinations. There are 7 executives in total, so we can choose 3 of them in (7 choose 3) ways. And out of those, we need to choose 2 men and 1 woman. Now, I could calculate it for you, but let's just say that the chances are a little bit like finding a unicorn riding a unicycle while juggling flaming balls.
D) Probability of 1 man and 2 women being selected:
Similar to the previous one, it's a matter of counting the combinations. We have 7 executives, and we want to choose 3, with 1 man and 2 women. The probability would be a bit higher than the previous one, but still not as high as finding a clown giving a serious business presentation!
Remember, in the end, it's all about balance and diversity. Who knows what wonderful ideas and perspectives might come from having a mix of men and women attending the seminar? So, let's hope for an inclusive and equally hilarious outcome!
To find the probabilities of selecting different combinations of executives, we need to use the concept of combinations and probability.
A) To find the probability that all 3 selected executives are men:
The total number of executives is 7, out of which 3 are men.
The number of ways to select all 3 men from 3 available men is 1 (since we can only select all of them).
The total number of ways to select any 3 executives from 7 available executives is given by the combination formula:
C(7, 3) = 7! / (3! * (7-3)!) = 35
Therefore, the probability of all 3 selected executives being men is:
P(A) = 1 / 35
B) To find the probability that all 3 selected executives are women:
The total number of executives is 7, out of which 4 are women.
The number of ways to select all 3 women from 4 available women is 1 (since we can only select all of them).
The total number of ways to select any 3 executives from 7 available executives is given by the combination formula:
C(7, 3) = 7! / (3! * (7-3)!) = 35
Therefore, the probability of all 3 selected executives being women is:
P(B) = 1 / 35
C) To find the probability that 2 men and 1 woman will be selected:
The total number of executives is 7, out of which 3 are men and 4 are women.
The number of ways to select 2 men out of 3 available men is given by the combination formula:
C(3, 2) = 3! / (2! * (3-2)!) = 3
The number of ways to select 1 woman out of 4 available women is given by the combination formula:
C(4, 1) = 4! / (1! * (4-1)!) = 4
Therefore, the total number of ways to select 2 men and 1 woman is:
C(3, 2) * C(4, 1) = 3 * 4 = 12
The total number of ways to select any 3 executives from 7 available executives is given by the combination formula:
C(7, 3) = 7! / (3! * (7-3)!) = 35
Therefore, the probability of selecting 2 men and 1 woman is:
P(C) = 12 / 35
D) To find the probability that 1 man and 2 women will be selected:
The total number of executives is 7, out of which 3 are men and 4 are women.
The number of ways to select 1 man from 3 available men is given by the combination formula:
C(3, 1) = 3! / (1! * (3-1)!) = 3
The number of ways to select 2 women from 4 available women is given by the combination formula:
C(4, 2) = 4! / (2! * (4-2)!) = 6
Therefore, the total number of ways to select 1 man and 2 women is:
C(3, 1) * C(4, 2) = 3 * 6 = 18
The total number of ways to select any 3 executives from 7 available executives is given by the combination formula:
C(7, 3) = 7! / (3! * (7-3)!) = 35
Therefore, the probability of selecting 1 man and 2 women is:
P(D) = 18 / 35
To find the probabilities, we need to use the concept of combinations.
The total number of ways to choose 3 executives out of 7 is calculated using the combination formula:
nCr = n! / (r!(n-r)!), where n is the total number of executives and r is the number of executives to be selected.
In this case, n = 7 (total number of executives) and r = 3 (number of executives to be selected).
A) All 3 selected are men:
The number of men in the company is 3, so the number of ways to choose 3 men out of 3 men is 1.
Therefore, the probability is 1/combination(7,3).
B) All 3 selected are women:
The number of women in the company is 4, so the number of ways to choose 3 women out of 4 women is 4C3 = 4.
Therefore, the probability is 4/combination(7,3).
C) 2 men and 1 woman will be selected:
The number of ways to choose 2 men out of 3 men is 3C2 = 3.
The number of ways to choose 1 woman out of 4 women is 4C1 = 4.
Since the selection of men and women is independent, we multiply the two possibilities: 3 * 4 = 12.
Therefore, the probability is 12/combination(7,3).
D) 1 man and 2 women will be selected:
The number of ways to choose 1 man out of 3 men is 3C1 = 3.
The number of ways to choose 2 women out of 4 women is 4C2 = 6.
Using the same logic as in part C, we multiply the two possibilities: 3 * 6 = 18.
Therefore, the probability is 18/combination(7,3).
To calculate the actual probabilities, we need to substitute the values into the combination formula and compute the denominators.