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Probability

This topic has 4 expert replies and 0 member replies

Probability

Post Sat Sep 16, 2017 7:26 pm
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

OA is a

why is E the only best option? which probability approach did you use to get your answer?[/spoiler]

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Post Sun Sep 17, 2017 5:12 pm
It seems like this is easy conceptually too. We want to pick both guys, so there's only one way to do that: 2 choose 2. If we're just picking two random guys, there are 6 choose 2, or 15 ways to do that, as shown in my previous post.

From there:

Our target = the one group
Our total = 6 choose 2 = 15 groups

Probability = target/total = 1/15

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Post Sun Sep 17, 2017 5:10 pm
We could also do All Groups - Groups With Neither Guy - Groups With Only One of the Guys:

All Groups = 6 choose 2 = 6!/(4!2!) = 15
Neither Guy = 4 choose 2 = 4!/(2!2!) = 6
Only One Guy = (4 choose 1) * (2 choose 1) = 8

If Only One Guy doesn't make sense, I'm choosing one of the other four people first, then choosing one of our two guys to go with them.

That leaves us with 15 - 6 - 8 = 1 group with both guys. 1 group out of 15 is 1/15, and we're done.

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Post Sun Sep 17, 2017 5:12 pm
It seems like this is easy conceptually too. We want to pick both guys, so there's only one way to do that: 2 choose 2. If we're just picking two random guys, there are 6 choose 2, or 15 ways to do that, as shown in my previous post.

From there:

Our target = the one group
Our total = 6 choose 2 = 15 groups

Probability = target/total = 1/15

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GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
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Post Sun Sep 17, 2017 5:10 pm
We could also do All Groups - Groups With Neither Guy - Groups With Only One of the Guys:

All Groups = 6 choose 2 = 6!/(4!2!) = 15
Neither Guy = 4 choose 2 = 4!/(2!2!) = 6
Only One Guy = (4 choose 1) * (2 choose 1) = 8

If Only One Guy doesn't make sense, I'm choosing one of the other four people first, then choosing one of our two guys to go with them.

That leaves us with 15 - 6 - 8 = 1 group with both guys. 1 group out of 15 is 1/15, and we're done.

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