Question

Probability that an applicant will have Master's degree is 1/3 and probability that he will not have work experience is 4/9. If the probability that he will have at least one characteristic is 1/5, what is the probability that he will have both characteristics?​

Answer 1

1/45

Explanation:

Let A be the event that the applicant has a Master's degree and B be the event that the applicant does not have work experience.

Then, we are given:

P(A) = 1/3

P(not B) = 4/9

P(at least one characteristic) = P(A or B) = 1/5

We want to find P(A and not B), which is the probability that the applicant has a Master's degree but no work experience.

Using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

We can rearrange to solve for P(A and B):

P(A and B) = P(A) + P(B) - P(A or B)

P(B) = 1 - P(not B) = 1 - 4/9 = 5/9

Substituting in the given probabilities:

1/5 = 1/3 + 5/9 - P(A and B)

Solving for P(A and B):

P(A and B) = 1/3 + 5/9 - 1/5

P(A and B) = 1/45

Therefore, the probability that the applicant will have both characteristics (a Master's degree and no work experience) is 1/45.