Question 514578: There are 65 students in a class, 32 are sophmores, 36 are history majors and 6 are neither.
(a) What is the probability that a student is both a sophmore and a history student
(b)Given the student is a sophmore, what is the propability the student is also a history major?
I believe there is a formula for this type of probabilty...poss like classic truth tables, this is a refresher for me.. not sure what type of formula or how to imput the information- Jessica
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw a big rectangle that represents the whole class. Since we know that 6 are neither Sophomore or History Majors, then we know from 65 - 6 that 59 are either one, the other, or possibly both. Since there are 32 sophomores and 36 history majors and the sum is 68 which is MORE than the total of 59, we know for certain that some of the 59 are actually sophomore history majors. Furthermore, since 68 minus 59 is 9, we know the number of sophomore history majors to be exactly 9.
Draw 2 circles that overlap partially inside of your rectangle. One of the circles will represent Sophomores and the other will represent History Majors. The overlap area will represent those students who are both. Put the number 9 in this overlap region. Since we know that 32 students are sophomores but 9 of those are also history majors, subtract 9 from 32 getting 23 which you now write in that part of the Sophomore circle that does not overlap. Likewise, put a 27 in the non-overlaped part of the History circle.
Now, just to check ourselves: 9 soph/hist major, 23 only soph, 27 only history, 6 none: 9 + 23 + 27 + 6 = 65 -- checks.
A) Pick one of the 65 students at random. 9 ways to successfully select a sophomore history major, ergo: 
B) Given that you have picked one of the sophomores, the denominator is reduced to the number of sophomores, i.e. 32, so: 
John
My calculator said it, I believe it, that settles it
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