SOLUTION: 30% of students at a university are freshmen. 20% went to high school in california. 7% are both. find the probability that a student is a freshmen who did not go to high school in

Algebra ->  Probability-and-statistics -> SOLUTION: 30% of students at a university are freshmen. 20% went to high school in california. 7% are both. find the probability that a student is a freshmen who did not go to high school in      Log On


   

Question 1061122: 30% of students at a university are freshmen. 20% went to high school in california. 7% are both. find the probability that a student is a freshmen who did not go to high school in california
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
probability that a student is a freshman is .30.
probability that a student went to high school in california is .20
probabilitt that a student went to high school in california and is a freshman is .07.

the assumption is that the student who went to high school and is a freshman is included in the totals of the student who is a freshman and is also included in the totals of the student who went to high school in california.

consequently, it needs to be subtracted from both and then added back in as a separate category.

subtracting it from both and adding as a separate category gets you.

students who are freshmen DISABLED_event_only= .23
students who went to a high school in california are .13
students who are freshmen and went to a high school in california are .07
total is .23 + .13 + .07 = .43

the probability that the student is a freshman who did not go to high school in california would be .23.

as an example:

assume 100 students.

30 are freshmen.
20 went to high school in california.
7 are freshmen who went to high school in california.

of the 30 freshmen, 7 also went to high school in california.
of the 20 who went to high school in california, 7 are freshmen.

the 7 are being counted twice.

take them out of each category and put them in their own category and you get the answer you are looking for.

30 = 23 + 7.
20 = 13 + 7.

the 7 are taken out and put in a separate category of both.

you get:
23 freshmen who did not go to high school in california.
13 from high school in california who are freshmen.
7 who are freshmen and from high school in california.