Lesson: Listing vs Counting vs Probability Rules

Comment on Listing vs Counting vs Probability Rules

At the 1:23 mark, why can't you follow the formula and 1/2 + 1/2?
greenlight-admin's picture

We could have continued that approach, but this video is all about examining our different options and probability questions involving "at least" are typically solved the fasted by using the complement.

That said, let's continue where we left off: P(1 heads) + P(2 heads)

We'll deal with each probability on its own.

P(1 heads) = P(1st toss heads and 2nd toss tails OR 1st toss tails and 2nd toss heads)
= P(1st toss heads and 2nd toss tails) + P(1st toss tails and 2nd toss heads)
= (1/2)(1/2) + (1/2)(1/2)
= 1/4 + 1/4
= 1/2

P(2 heads) = P(1st toss heads AND 2nd toss heads)
= (1/2)(1/2)
= 1/4

So, P(1 heads) + P(2 heads) = 1/2 + 1/4 = 3/4

6C2/10C2.. Can you solve it in detail.. I mean do we have to simplify it like 6C2=180...Or there is a shortcut to solve this
greenlight-admin's picture

Yes, there is definitely a shortcut.
Here's the video that explains how you can calculate 6C2 and 10C2 in your head: https://www.greenlighttestprep.com/module/gre-counting/video/789


I got it.. Thanks

Hello Brent,

I solved the question as follows
Joe is in a group consisting of N people (N > 4).

If 3 people from the group are randomly selected to be on a committee, what is the probability that Joe is selected?

I assument N = 5 , there are total of 5C3 was to select people , this is my denominator that is 1/10.
Now i have to choose Joe so 1 way now remaining 2 people can be selected in 4C2 ways that is (1 X 4 X 3)/ (2 X 1) which comes to 6.

SO final answer is 6/10 = 3/5 hence option C. am i right.
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/joe-is-in-a-group-consisting-of-n-peopl...

You're using the INPUT-OUTPUT approach to solve this question (covered here: https://www.greenlighttestprep.com/module/gre-word-problems/video/936)

When N = 5, the probability = 3/5

At this point, we must check ALL 5 answer to see which one(s) evaluate to be 3/5 when N = 5

A) When N = 5, (N²−2N−6)/(N−2)²+6 = 3/5
C) When N = 5, N/5 = 3/5

So, the correct answer is EITHER A or C.

From here, you must test a different value of N to determine the correct answer.


Hi Brent,
In the last question of Reinforcement Activities, click on the link GRE practice question (difficulty level: 160 to 170) – Greenlight Test Prep
Instead of asking of what is the probability that Joe is selected, he is asking what is the probabilty of selection three people, what would be the answer to this question?
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/joe-is-in-a-group-consisting-of-n-peopl...

Sorry, but I'm not sure what you mean by "probability of selection three people"
Can you please elaborate?

It's great how you can try multiple approached to get the same answer with probability questions. The only issue I see here is which approach is the shortest. I don't think you can accurately assess that in the beginning. When you start with 1 approach, it's best to just carry it out to the end. However long it takes, it takes, and just hope that you get the right answer. If you get stuck, then you'll have to try a different approach if you can, which still eats up time. Really, the greatest enemy on the GRE is time. I keep coming back to this theme again and again.
greenlight-admin's picture

Good points.
In general, I find that applying probability rules is typically faster than using counting techniques.

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