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## Comment on

Listing vs Counting vs Probability Rules## At the 1:23 mark, why can't

## We could have continued that

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

## Yes, there is definitely a

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

Cheers,

Brent

## 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.

## Question link: https:/

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.

Cheers,

Brent

## 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?

## Question link: https:/

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

## Good points.

Good points.

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