On December 20, 2023, Brent will stop offering office hours.
- 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
- Blog
- Philosophy
- 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
Hi Brent,
if the statement 2 states that: probability of selecting a white ball is equal to 0.2
Whether this statement would be sufficient?
Thanks
Okay, let's change the
Okay, let's change the question so that we have:
(2) P(selecting white) = 0.2
In this case, statement 2 it's still insufficient. Consider these two conflicting cases:
CASE A: It could be the case that there are 10 balls in total such that 6 are green, 2 are white, and 2 are red.
In this case, P(green or red) = 8/10
CASE B: It could be the case that there are 10 balls in total such that 6 are green, 2 are white, 1 is red, and 1 is yellow.
In this case, P(green or red) = 7/10
Does that help?
Got it. Thanks
Thanks