Four hundred people apply for three jobs. 130 of the applicants are women.
(a) If three persons are selected at random, what is the probability that all are women? (Round the answer to six decimal places.)
(b) If three persons are selected at random, what is the probability that two are women? (Round the answer to six decimal places.)
(c) If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)
(d) If three persons are selected at random, what is the probability that none is a woman? (Round the answer to six decimal places.)
To solve this problem, we need to determine the total number of possibilities and the number of desired outcomes for each question.
First, let's calculate the total number of ways to select three people from a pool of 400 applicants. This can be done using the combination formula:
nCr = n! / [(n-r)! * r!]
For selecting three people from 400 applicants, we have:
Total number of ways = 400C3 = 400! / [(400-3)! * 3!]
Now, let's proceed to answer each question separately:
(a) Probability that all three selected are women:
In this case, the number of desired outcomes is the number of ways to select three women from a pool of 130 applicants, which is given by 130C3.
Probability = Number of desired outcomes / Total number of ways
= 130C3 / 400C3
To calculate this probability, you can use a calculator or a statistical software that supports combinations.
(b) Probability that two selected are women:
In this case, we need to consider all the possible ways of selecting two women and one man. The number of desired outcomes would be the product of 130C2 (to select two women from 130) and 270C1 (to select one man from the remaining 270).
Probability = Number of desired outcomes / Total number of ways
= (130C2 * 270C1) / 400C3
(c) Probability that one selected is a woman:
Here, we consider all the possible ways of selecting one woman and two men. The number of desired outcomes would be the product of 130C1 (to select one woman from 130) and 270C2 (to select two men from the remaining 270).
Probability = Number of desired outcomes / Total number of ways
= (130C1 * 270C2) / 400C3
(d) Probability that none selected is a woman:
In this case, we need to select three men from the pool of 270 male applicants. The number of desired outcomes is given by 270C3.
Probability = Number of desired outcomes / Total number of ways
= 270C3 / 400C3
To calculate the probabilities in (a), (b), (c), and (d), you can use a calculator or a statistical software that supports combinations and division to obtain the decimal values. Round the final answers to six decimal places.
130 women, 270 men
a) Prob(3 women) = C(130,3)/C(400,3) = 357760/10586800 = .033793
b) Prob(2 women 1 man) = C(130,2)xC(400,1)/C(400,3) = .316810
can you see how I am doing those?
see if you answer the last two yourself.