Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.
See classesLearn live with an expert or move at your own pace. Every option includes the complete TTP study system.
Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.
with Josh Braslow, 20+ years in test prep
Self-paced EA prep. Study on your schedule.
with
Complete access from day one. Study on your schedule.
Hi sud21!sud21 wrote:
Whitney Garner wrote:Hi sud21!sud21 wrote:
I would be very leery of questions posted from unknown sources. Unfortunately, there is no way to answer this question in the form given. We might think this is as simple as multiplying the Pr(NOT A) times Pr(NOT B) = 1/5, but this will not always be the case. We need to know more about the events in terms of their dependence. Here are 2 examples of what I mean.
For the following 2 examples, let's pretend that we have a 10 sided die with the numbers 1-10 on the sides (to keep the probabilities the same.
Example 1
Event A = rolling an even number (2, 4, 6, 8, 10 are successes) = 0.5 probability
Event B = rolling a number >=5 (5, 6, 7, 8, 9, 10 are successes) = 0.6 probability
Now, if we use simple formulas:
Pr(A&B) = (0.5)(0.6) = 0.3
Pr(A only) = Pr(A & NOT B) = (0.5)(1-0.6) = (0.5)(0.4) = 0.2
Pr(B only) = Pr(B & NOT A) = (0.6)(1-0.5) = (0.6)(0.5) = 0.3
Pr(Neither) = Pr(NOT A & NOT B) = (1-0.5)(1-0.6) = (0.5)(0.4) = 0.2
Let's check this by looking at the actual outcomes for each probability:
Pr(A&B) = (6, 8, 10) = 3/10 = 0.3
Pr(A only) = (2, 4) = 2/10 = 0.2
Pr(B only) = (5, 7, 9) = 3/10 = 0.3
Pr(Neither) = (1, 3) = 2/10 = 0.2
These all check out, so it would seem as if the basic formulas work...BUT, what if we change the definition of event A...
Example 2
Event A = rolling a number >=6 = (6, 7, 8, 9, 10) = 0.5 probability
Event B = rolling a number >=5 = (5, 6, 7, 8, 9, 10) = 0.6 probability
The probabilities we calculated above would still be the same mathematically...but when we actually look at the results, we see that they SHOULD be different:
Pr(A&B) = (6, 7, 8, 9, 10) = 5/10 = 0.5
Pr(A only) = (empty) = 0.0
Pr(B only) = (5) = 1/10 = 0.1
Pr(Neither) = (1, 2, 3, 4) = 4/10 = 0.4
So you can see, there is no way to answer this question unless we know that the events are "independent"!
Whit
Hi Pemdas!pemdas wrote:whuttttt? are you deducting and finding complement for p(A) as 1-0.6 and p(B) as 1-0.5 ??
what are you talking about here? they are not mutually exclusive as p(A)+p(B)>1 Hence you had to account for their *joint* probability
this is a normal question and the answer is 0.4
in fact we would benefit from applying some set concepts into this probability as well; p(A)=0.6 and p(B)=0.5 The probability for not A neither B will be max.favorable/total outcome
total outcome is 1 (100%), max favorable p(not A+not B) is 1-(0.6-0.5)-0.5 implying there are 50% A and B, and of this 50% additional 10% only A leaving out p(not A+not B) as 40% or 0.4
c
why you talk about dependence/independence here stays guess for me, as we don't even draw any trials here like with dices in your very detailed explanation. Dependent/independent is useful for *without replacement* and *with replacement* accordingly.
Whitney Garner wrote:Hi Pemdas!
I'm sorry if the language in my earlier reply wasn't 100% clear. You are exactly right that we need to be concerned about the Joint probability, because without it, there is no way to answer this question. You assumed that the joint probability must be the simple overlap (0.1), but from the 2 examples I provided, just because one event has a probability of 0.6 and the other has a probability of 0.5, we cannot draw any conclusions on their "overlap" (or joint likelihood). In both examples, the events I provided had the same probabilities as the original question, but in example 1 the joint probability was 0.3 (some overlap) while in example 2 it was 0.5 (perfect overlap). This results in 2 very different answers for the probability of Neither.
I also understand that my examples might have caused confusion because they are not as simply stated as the original. I wanted to use real world example events to indicate the various levels of "overlap" that might occur. This is always something we should consider. If the original had told us that each occurred with a probability of 0.5, we CANNOT assume that they are mutually exclusive just because they sum to 1. The point is that to find the probability of NEITHER, we would need more information, this problem is Incomplete.
I hope this clears up the confusion from my earlier response!
Whit
Hi Pemdas!pemdas wrote:I haven't said it's 10% (0.1) rather I put 0.5 as overlap. 0.1 is P(Only event A occurs). 0.5 is P(A&B) and 0.4 is P(Not A+B).
Glad to help - just remember that on the GMAT we CANNOT ever assume!pemdas wrote:Whitney Garner, I hear you
the joint probability P(A∩B) equal to 0.6*0.5=0.3 will be valid if A and B are independent, that's what you meant?
then we safely consider P(Neither A nor B) as equal to 1-(0.6+0.5-0.3)=0.2. Since no information about the independence of A on B (conversely, B on A) has been provided this question fell under my assumption about P(A∩B).
Well let's consider then it has solution as answer A if the independence of A on B is assured, in other cases we have to look into P(A∩B)
thanks for contributing in this thread, your posts were very much useful as they helped me clear the things out
