Question: Yellow Ball or Red Ball

Comment on Yellow Ball or Red Ball

Is there a way we can use the equation used in statement one to prove that statement 2 is sufficient?
gmat-admin's picture

When analyzing the sufficiency of each statement, we cannot use information from a different statement.

Hi - Can all probability questions be solved using permutations and combination methods?
gmat-admin's picture

True permutation questions are VERY rare on the GMAT. In fact, I write about this here:

In the article, I write:

"I’ve never been a big fan of the phrase “Combinations and Permutations.” It suggests that all counting questions can be solved using either combinations or permutations, when this is not so."

I will say that counting questions can typically be solved using the Fundamental Counting Principle (FCP), or combinations, or a mixture of combinations and FCP.

ari.banerjee's picture

Hi Brent,

I am really confused here.

How did you not select P(R&Y) in the equation:

P(RorY)=P(R) + P (Y) - P(R&Y)

By not selecting we are assuming that these are mutually exclusive events? But the selection of Y does depend on the selection of R and vice versa as the total no: of balls inside the box will decrease? The question doesn't mention with replacements either?

In that case how would statement 2 alone be enough to solve for the question?

Also, P(not g) can also mean P(r&r) and P(y&y). Why did you only chose P(YorR)?

Can you please explain what is it that I am missing?

Thank you!
gmat-admin's picture

There's nothing wrong with the approach that you're suggesting. The problem is that it doesn't help with statement 2.

With many probability questions, we can choose to use counting methods OR we can choose to use probability rules.
I chose to represent P(R or Y) using counting methods (i.e., the number of each colored ball)

If we go with probability rules (your approach), our target question becomes: What is the value of P(R) + P(Y) - P(R and Y)?

Statement 1 tells us that P(R) = 1/4
So, we now know that P(R) + P(Y) - P(R and Y) = 1/4 + P(Y) - P(R and Y)
Since we're still missing the values of P(Y) and P(R and Y), we can't answer the target question.
So, statement 1 is NOT sufficient.

Now onto statement 2, which tells us that P(green) = 2/5
Hmmm, what are we supposed to do with this information?
It certainly doesn't SEEM to help us determine the value of P(R) + P(Y) - P(R and Y)

At this point, we need to recognize that the statement 2 information, P(green) = 2/5, doesn't really fit into our chosen approach, which means we should look for a different approach (or guess and move on :-)

If we choose to abandon the probability rules approach, then we might come up with an approach that's similar to the solution presented in the video.

Does that help?


ari.banerjee's picture

I am still a bit perplexed. Isn't this is a value question?

As it asking you a value for the probability? So any statement that doesn't give you a distinct answer is insufficient?

The problem is that if you go by the probability rules then the two statements become insufficient to solve the qs. So option E seems correct but if I use your method to ignore the probability rules then I get option B.

Is this an official GMAT qs? Can we expect a confusion like this on the real test?
gmat-admin's picture

We can't say that using probability rules results in statement 2 being insufficient.
The real problem is that, if we use probability rules, we don't really know what to do with statement 2, because it doesn't fit the narrow approach we've decided to use.
Not knowing what to do with a statement is not the same as concluding that the statement is insufficient.

So, a different approach is required here.

Notice that we can take statement 2 and conclude that, if P(selecting green ball) = 2/5, then P(NOT selecting green ball) = 1 - 2/5 = 3/5

So, we know that P(NOT selecting green ball) = 3/5.
How does this help us find P(selecting a ball that is red or yellow)?

At this point, we must recognize that, if the ball we select is NOT green, then that ball is either red or yellow.
In other words, P(NOT selecting green ball) = P(selecting a ball that's either red or yellow)

So, if P(NOT selecting green ball) = 3/5, then P(selecting a ball that's either red or yellow) = 3/5 as well

"Is this an official GMAT qs? Can we expect a confusion like this on the real test?"
This question is based on a real GMAT question, which applies the same principle.
As such, this could definitely be a question that could appear on test day.


Hi Brent,

I had a question regarding this question:

In the solution, one needs to use the equation P(A) + P(B) - P(A&B) = P(A or B)
However, I was under the impression that this equation can only be used for independent events.

How can we assume in the problem linked above that the color and number of the ball are independent?

gmat-admin's picture

Question link:

I think you're confusing "independent" with "mutual exclusive"

If two event are independent, then P(A AND B) = P(A) x P(B)
If two event are mutually exclusive, then P(A OR B) = P(A) + P(B)

That said, the formula P(A or B) = P(A) + P(B) - P(A&B) works for all OR probabilities.
However, hen the two events are mutually exclusive, then P(A&B) = 0

Does that help?


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