What is the probability

[statpr226]

The probability that a student takes statistics course in the first semester is 67% and the probability that he takes Corporate Finances course is 52%. The probability that a student takes both in the first semester is 30%. What is the probability that a student takeseither Statistics or Corporate Finances?

It's a question from the class, I tried but it doesn't work. Anything you can do to help! Thanks

 

[HallsofIvy]

Imagine 1000 students. 67%, 670 students, take Statistics. 52%, 520 students, take Corporate Finances. 30%, 300 students, take both.

So 670- 300= 370 students take statistics but not Corporate Finances.

520- 300= 220 students take Corporate finances but not Statistics.

That is a total of 370+ 220+ 300= 890 students out of 1000, 89%, who take at least one of Statistics or Corporate Finances.

 

[JeffM]

Just keep in mind one of the basic laws of probability.

[MATH]\text {P(A or B) = P(A) + P(B) - P(A and B)}.[/MATH]
[MATH]0.67 + 0.52 - 0.30 = 0.89 = 89\%.[/MATH]
Halls of Ivy showed why that law makes sense in your specific case, but it is really one of those things that you should know in a flash.

 

[statpr226]

thnks

 

[lex]

@statpr226
For your method to have worked you would need A and B to be independent.
We know they are not because:
[MATH]P(A\cap B)\neq P(A)\times P(B) [/MATH]

 

[Dr.Peterson]

The probability that a student takes statistics course in the first semester is 67% and the probability that he takes Corporate Finances course is 52%. The probability that a student takes both in the first semester is 30%. What is the probability that a student takeseither Statistics or Corporate Finances?
View attachment 25923
It's a question from the class, I tried but it doesn't work. Anything you can do to help! Thanks

Another problem in your work is that you are trying to calculate only "takes Statistics but not Corporate Finance" and "takes Corporate Finance but not Statistics". If you add these together (and if they had in fact been independent), you would have calculated "takes only one of the two courses". That is not the same as "takes either Statistics or Corporate Finance", which in this sort of question also includes "takes both". (Note that they told you clearly that they are not mutually exclusive; and if, as you wrongly assumed, they were independent, then they could not be mutually exclusive either.)