Have questions about your preparation or an upcoming test? Need help modifying the Study Plan to meet your unique needs? No problem. Just book a Skype meeting with Brent to discuss these and any other questions you may have.

- Video Course
- Video Course Overview
- General GMAT Strategies - 7 videos (free)
- Data Sufficiency - 16 videos (free)
- Arithmetic - 38 videos
- Powers and Roots - 36 videos
- Algebra and Equation Solving - 73 videos
- Word Problems - 48 videos
- Geometry - 42 videos
- Integer Properties - 38 videos
- Statistics - 20 videos
- Counting - 27 videos
- Probability - 23 videos
- Analytical Writing Assessment - 5 videos (free)
- Reading Comprehension - 10 videos (free)
- Critical Reasoning - 38 videos
- Sentence Correction - 70 videos
- Integrated Reasoning - 17 videos

- Study Guide
- Your Instructor
- Office Hours
- Extras
- Prices

## Comment on

Red or Green Ball## thanks for this video

## Can anyone please sugest why

## We need not assume that the

We need not assume that the box contains only red and green balls,

Instead, we are applying the fact that a probability can never exceed 1. In the given information we're told that P(selecting a green ball) = 0.6

Then statement 1 tells us that P(selecting a red ball) = a value that's greater than or equal to 0.4

Since P(selecting a green ball OR red ball) = P(selecting a green ball) + P(selecting a red ball)

= 0.6 + (a probability that's greater than or equal to 0.4)

Since this sum cannot exceed 1, we can conclude that P(selecting a red ball) = 0.4

This means that P(selecting a green ball OR red ball) = 1

In other words, we a GUARANTEED to select a green or red ball. So, we can conclude that the box contains ONLY red and green balls.

So, we aren't ASSUMING that the box contains only red and green balls; we're CONCLUDING that the box contains ONLY red and green balls.

## I really got confused between

## You might want to review the

You might want to review the video on mutually exclusive events: https://www.gmatprepnow.com/module/gmat-probability/video/746

That should help.

## I used to think whenever a

Is this a special case for probability?

Please kindly clarify

Ademini

## Statement 1 yields more than

Statement 1 yields more than one possible value for P(R), however only one solution is valid.

Consider this analogous question:

Gwen owns Q rabbits. What is the value of Q

(1) Q² = 25

(2) some other fact

STATEMENT 1: When we solve the equation Q² = 25, we find that EITHER Q = 5 OR Q = -5

Since we have two possible values for Q, does this mean statement 1 is insufficient?

No. The solution Q = -5 is invalid, since one cannot own -5 rabbits.

So, statement 1 is sufficient.

Likewise, in the video question, P(R) cannot be greater than greater than 0.4. So, it must be the case that P(r) = 0.4, which means statement 1 is sufficient.

Does that help?

Cheers,

Brent

## so, we are not taking the 2nd

So answers will vary?

## That's correct.

That's correct.

## Hi Brent,

Could you please explain why statement two is insufficient?

Many thanks

## I'm happy to help.

I'm happy to help.

For statement 2, consider these two conflicting cases:

CASE A: There are 6 green balls, 0 red balls and 4 white balls.

Notice that P(green) = 6/10 = 0.6 [satisfies given info]

And P(white) = 4/10 = 0.4 [satisfies given info]

In this case, the answer to the target question is "P(red or green) = 6/10"

CASE B: There are 6 green balls, 1 red ball and 3 white balls.

Notice that P(green) = 6/10 = 0.6 [satisfies given info]

And P(white) = 3/10 = 0.3 [satisfies given info]

In this case, the answer to the target question is "P(red or green) = 7/10"

Since we cannot answer the target question with certainty, statement 1 is not sufficient.

Does that help?

Cheers,

Brent

## Add a comment