Roland2rule wrote:Joshua and Jose work at an auto repair center with 4 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
A. 1/15
B. 1/12
C. 1/9
D. 1/6
E. 1/3
Approach 1:
From the 6 workers, the number of combinations of 2 that can be formed = 6C2 = (6*5)/(2*1) = 15.
Of these 15 pairs, only 1 is good: Joshua and Jose.
Thus:
P(Joshua and Jose are both chosen) = 1/15.
Approach 2:
Joshua and Jose constitute 2 of the 6 workers.
Thus:
P(Joshua or Jose is chosen on the 1st pick) = 2/6.
Since Joshua or Jose is chosen on the 1st pick, only 1 of the 5 remaining workers will be Joshua or Jose.
Thus:
P(Joshua or Jose is chosen on the 2nd pick) = 1/5.
Since we want both events to happen, we multiply the probabilities:
P(Joshua and Jose are both chosen) = 2/6 * 1/5 = 1/15.
The correct answer is
A.
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
