study wrote:
can someone explain how to solve this problem the direct way.
I did the following, but didnt get to the right answer. What is wrong in my method?
6/8 * 5/7 = 30/56 = 15/28
The problem below is similar. And the answer is 8/10. So why cant the answer to the above be 6/8*5/7 ?
10 applicants are interviewed for a position. Among them are Paul and Jen. If a randomly chosen applicant is invited to interview first, what is the probability to have neither Paul nor Jen at the first interview?
* \(\frac{1}{10}\)
* \(\frac{1}{9}\)
* \(\frac{1}{2}\)
* \(\frac{8}{10}\)
* \(\frac{9}{10}\)
Yup, that's the trick in the language of the posted question. Read the last line again - "what is the probability of not picking
exactly two tulips"? The "exactly" 2 tulips means that one of them can be a tulip but both can't be tulips. So what happens when you do 6/8 * 5/7 is that possibilities in which only one of the flowers is a tulip do not get counted.
So that's why the right approach is to subtract the possibility of getting exactly two tulips from the "entire universe" of possible options, because that will include possibilities of one tulip as well.
Good thing is none of the answer choices is 15/28, so you can figure out that you have gone wrong somewhere, but knowing the makers of the GMAT, I am sure that's not a luxury which will offered to you on the test day (i.e. they will most certainly include 15/28 as an option)