# Lesson: Listing vs Counting vs Probability Rules

## Comment on Listing vs Counting vs Probability Rules

### At the 1:23 mark, why can't

At the 1:23 mark, why can't you follow the formula and 1/2 + 1/2?

### 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

= (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

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

### 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

I got it.. Thanks

### Hello Brent,

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.

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,

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?

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