Question: Red or Green Ball

Comment on Red or Green Ball

thanks for this video

Can anyone please sugest why are we assuming initially that we have only red and green balls in the box which makes us believe that testament A is sufficient.
gmat-admin's picture

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 the inclusive and exclusive part and when we have to remove p(A +B) from the formula
gmat-admin's picture

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

That should help.

ademini's picture

I used to think whenever a statement yield more than one possible answer the statement is not sufficient, like in quadratic equations most are rejected for conflict facts but here we are ignoring the OR to maintain that one of the possible answers is sufficient.
Is this a special case for probability?
Please kindly clarify

Ademini
gmat-admin's picture

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 statement because the probability of selecting a white can be either 0.4, 0.3, 0.2 or 0.1?

So answers will vary?
gmat-admin's picture

That's correct.

Hi Brent,

Could you please explain why statement two is insufficient?

Many thanks
gmat-admin's picture

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

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