More than three-quarters of the nation’s colleges and universities now offer online classes, and about 23% of college graduates have taken a course online. 39% of those who have taken a course online believe that online courses provide the same educational value as one taken in person, a view shared by only 27% of those who have not taken an online course. At a coffee shop you overhear a recent college graduate discussing that she doesn’t believe that online courses provide the same educational value as one taken in person. What’s the probability that she has taken an online course before?
0.2079
0.1997
0.3014
0.1403
I have an answer which is wrong apparently but I don't understand why.
Can a maths whizz give the correct answer with an idiots' explanation as to why?
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Comments
Your second one is correct so why?
23% have done a course online so 23,000. 39% of those (8,970) believe it has the same value, 61% (14,030) think it doesn't
77% (77,000) haven't done a course online. 27% (20,790) think it has the same value, 73% (56,210) don't
so there are 70, 240 who don't believe the courses have the same value. of those 14, 030 have done an online course
14, 030 is 19.97% of 70, 240 so 0.1997
Imagine there are 100 graduates: 23 of them have taken an online course, 77 haven't
Of the 23 who have taken an online course, 61% are 'non-believers' - that's 14.03 non-believers (23 x 61%)
Of the 77 who haven't taken an online course, 73% are non-believers - that's 56.21 non-believers (77 x 73%)
So of our 100 students, we have 70.24 'non-believers' (14.03 + 56.21). 14.03 of these have taken an online course, so the probability is .1997 (14.03 divided by 70.24)
she's either
a) taken a course and disagrees it offers the same value, or
b) not taken a course and disagrees it offers the same value.
The total probability that someone would disagree is that
a) There's a 23% chance she HAS taken a course, and of that a 61% chance she disagrees which is overall a 14.03% chance PLUS
b) There is a 77% chance she has not taken a course, and a further 73% chance she disagrees which is overall a 56.21% chance
So the the total probability is 70.24% of which 14.03% is that she has taken the course. 14.03% of 70.24% is 19.97%.
I dont feel I have explained this very clearly, but I have work to do.
Your explanations both make sense.
After many years of not doing this stuff I've now remembered that read the question CAREFULLY is fundamental!!
:-)