Six candidates for a new position of vice-president for academic affairs have been selected. Three of the candidates are female. The candidates’ years of experience are as follows.
Candidate Experience
Female 1
Female 2
Female 3
Male 1
Male 2
Male 3
5
9
11
6
4
8
Suppose one of the candidates is selected at random. Define the following events:
A = person selected has 9 years experience
B = person selected is a female
Find P(A / B).
A) 0.4552
B) 0.333
C) 0.581
D) 0.418
From your data, you have 6 candidates, with 2 having 9+ years of experience and 3 being female. This should give you the probabilities of A and B. Assuming you want to know what is the probability that the candidate will be both experienced and female, multiply the two probabilities.
I hope this helps. Thanks for asking.
To find the conditional probability P(A/B), we need to use the formula:
P(A/B) = P(A ∩ B) / P(B)
First, let's find P(A ∩ B), which represents the probability that the selected candidate is both female and has 9 years of experience.
Among the six candidates, there are three females. We are looking for the probability of selecting a female candidate with 9 years of experience. Looking at the table, we see that only Female 2 has 9 years of experience.
So P(A ∩ B) = 1 out of 6, as there is only one candidate who satisfies both conditions.
Next, let's find P(B), which represents the probability that the selected candidate is a female.
There are three female candidates out of six total candidates.
So P(B) = 3 out of 6, which simplifies to 0.5.
Now we can calculate P(A/B) using the formula:
P(A/B) = P(A ∩ B) / P(B)
P(A/B) = (1/6) / (1/2)
= (1/6) * (2/1)
= 1/3
Therefore, the answer is B) 0.333.