Probability of exactly one?

#1
Hello, I have a question that I am stuck on.
Given: the probability of passing a Photography class is 75% and the probability of passing a Economics class is 65%. The probability of passing at least one test is 85%. The question asks for the probability of passing exactly one test.
I tried using binomial probability formula, but that one doesn't work because it uses the success and failure of just one event, not two...
Any help would be appreciated...

And btw, the answer to that is 60%... I just don't know how to get to that percentage...
 
#2
i got 42.5%. not sure but:

pass photography but fail the other topic:16.25%
fail photography but pass the other topic: 26.25%

also, pass both 48.75%
fail both: 8.75%

all add up to 100%
 
#4
recall that P(a or b) = P(a) + P(b) - P (a and b) given that you know p(a or b) and P(a) and P(b) you can solve for P(a and b). now use a venn diagram and you should find your answer easily.

good luck
jerry
 
#5
Ok, so using the formal addition rule, P(A or B) = P(A) + P(B) - P(A and B)

So if I understood it right this is what I should do:
P(Photography or Economics) = P(Photography) + P(Economics) - P(Photography and Economics)
.85=.75 + .65 - P(A and B)
= .55

So the probability of passing exactly one is 55%?
It doesn't seem to coincide with the 60% given in the answer key for that problem...
Using the venn diagram, as i understand, is something like this chart I quickly drew up by hand:
:confused:
 
#7
Oops, I forgot to subtract the joint portion in the venn diagram... But that still doesn't solve it...
So .75 - .55= .2 and .65 - .55= .1
.1 + .2 = .3 = 30% chance of passing exactly one test?
 

Dragan

Super Moderator
#9
Oops, I forgot to subtract the joint portion in the venn diagram... But that still doesn't solve it...
So .75 - .55= .2 and .65 - .55= .1
.1 + .2 = .3 = 30% chance of passing exactly one test?
So...How many tests are given to determine if one passes a class?...Look at your original question (above).