Out of 200 applicants for a job, 125 are female, 100 have a graduate degree, and 75 are female and have a graduate degree. If an applicant is chosen at random, find:
a) The probability they are female or have a graduate degree.
It isn't something as easy as 125/200 for female and 75/200 for having a graduate right?
125/200 female, 100/200 graduate degree (regardless of gender)
P(F or G) = P(F) + P(G) - P(F and G). As you can see, you must subtract out the probability of the overlapping event to get the right answer.
P(F and G) = P(F) * P(G).
I see, so it would be P(F or G): 125/200 + 100/200 - (125/200* 100/200)= 13/16?
Also, I'm assuming then if I were to find the conditional probability they have a graduate degree given they are female, then it would just be (125/200* 100/200)?
Oh no wait nvm...it would be 15/64 for the conditional probability I think.
No, it's not as straightforward as just dividing the number of females by the total number of applicants and the number of applicants with graduate degrees by the total number of applicants. To find the probability that an applicant is female or has a graduate degree, we need to consider the overlap between the two groups.
To find the probability, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
In this case, A represents being female and B represents having a graduate degree.
P(A) = number of females / total number of applicants = 125 / 200 = 0.625
P(B) = number with a graduate degree / total number of applicants = 100 / 200 = 0.5
P(A and B) = number of females with a graduate degree / total number of applicants = 75 / 200 = 0.375
Now we can substitute these values into the formula:
P(A or B) = P(A) + P(B) - P(A and B)
= 0.625 + 0.5 - 0.375
= 0.75
Therefore, the probability that an applicant is female or has a graduate degree is 0.75 or 75%.