BTGmoderatorDC wrote:Two thirds of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 1/6
(B) 1/4
(C) 2/3
(D) 3/4
(E) 11/12
P(at least one of the 2 selected roads is at least 5 miles long) = 1 - P(neither of the 2 selected roads is at least 5 miles long)
From A to B:
Since 2/3 of the roads are at least 5 miles long, 1/3 are not.
Thus, the probability of selecting a road that is not at least 5 miles long = 1/3.
From B to C:
Since 1/4 of the roads are at least 5 miles long, 3/4 are not.
Thus, the probability of selecting a road that is not at least 5 miles long = 3/4.
P(neither of the 2 selected roads is at least 5 miles long) = (1/3)(3/4) = 1/4.
Thus:
P(at least one of the 2 selected roads is at least 5 miles long) = 1 - 1/4 = 3/4.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
