According to a prominent investment adviser, Company X has a 50% chanc

Question

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for  Least probability for both  the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for  Greatest probability for both  the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

ID: 700202

mike12543 · Accepted Answer

i am not sure whether i know math after seeing this question.

MartyMurray · Answer

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

An intuitive way to handle this question is to see the following.

The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.

Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.

If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.

In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.

So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.

Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.

Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.

So, the correct answer for Greatest Probability for Both is 50%.

Correct Answer: 10%, 50%

KarishmaB · Answer

We do not know the relation between the two events. We cannot say that they must be independent. Whay if both companies have the same suppliers and markets? There could be a strong correlation between their chance of posting profits. Or the two companies could be totally independent. The point is, we do not know the relation between the two events.

Probability works just as Sets does.

Minimum: 
Both and Neither move together. For Both to be minimum, Neither = 0
P(X or Y) = P(X) + P(Y) - P(Both)
P(X or Y) = .5 + .6 - P(Both)
For P(Both) to be minimum, P(X or Y) must be maximum i.e. 1. 
1 = .5 + .6 - P(Both)
P(Both) = .1

Maximum: 
P(Both) cannot be greater than either one individually so maximum value of P(Both) will be .5

Hence, select 10% and 50%.

How Both and Neither work together in Overlapping Sets is discussed in  this video  on my  YouTube channel .

chienp054 · Answer

OFFICIAL EXPLANATION    
Infer
RO1, Least probability for both:
To determine what the least probability is of both Company X and Company Y posting a profit in the coming year, determine what is the greatest probability of one of the companies—say Company X—posting a profit and the other company—Company Y—not posting a profit, and then subtract that result from the probability of Company X posting a profit. Because the probability of Company Y posting a profit in the coming year is 60%, then the probability of Company Y not posting a profit in the coming year is 40%. The greatest probability of Company X posting a profit and Company Y not posting a profit in the coming year cannot exceed the lesser of the probability of Company X posting a profit in the coming year—which is 50%—and the probability of Company Y not posting a profit in the coming year—which is 40%. Therefore, at most, the probability of both Company X posting a profit but Company Y not posting a profit in the coming year is 40%. Subtracting the 40% probability of Company X posting a profit from the probability of Company Y not posting a profit from the 50% probability of Company X posting a profit gives us the least probability of both Company X and Company Y posting a profit in the coming year, namely 10%.

The correct answer is 10%.

RO2, Greatest probability for both:
The greatest probability of both Company X and Company Y posting a profit in the coming year cannot exceed the lesser of the probability of Company X posting a profit in the coming year—which is 50%—and the probability of Company Y posting a profit in the coming year—which is 60%. Therefore, the greatest probability of both Company X and Company Y posting a profit in the coming year is 50%.

The correct answer is 50%.

This is the official answer. I'm trying to wrap my head around it as well. So if anyone can care to dumb it down for me. That will be appreciated!

mayankdgmat · Answer

It will be 10,50 100=60+50-both+neither both=10+neither neither can be 0 and max 40 if 50 is complete overlap in 60 https://gmatclub.com/forum/download/file.php?id=81800 GMAT-Club-Forum-87pb99o0.png

kittle · Answer

MartyMurray  - would you recommend skipping this question in exam? I was not able to wrap my head around how to solve this.

MartyMurray · Answer

I'd recommend learning how to answer this question, which isn't very complex actually, because there are at least two questions that work like this one on the Focus Edition practice tests. So, it appears that GMAC's question-writers may be into involving this concept in questions.

manasp35 · Answer

Different Approach (for understanding purpose)

Let
x = only X is profitable
y = only Y is profitable
b = both profitable
a = none are profitable

Given
x + b = 50 meaning b = 50 - x , according to this
b max is 50, b min is 0 --- eq 1
y + b = 40 meaning b = 40 - y , according to this
b max is 40, b min is 0 -- eq 2

Adding above equations, x + y + 2b = 90

x + y + a + b = 100
but x + y = 90 -2b

90 - 2b + a + b = 100
b = a - 10 , according to this
b max is 90, b min is 0 ---- eq 3

combining eq 1, eq 2, eq 3. Since b needs to satisfy all three equations
b max is 40 , b min is 0.

KarishmaB · Answer

The rules of probability are similar to those of Sets. P(X) = 50% P(Y) = 60% P(X or Y) = P(X) + P(Y) - Both Both = P(X) + P(Y) - P(X or Y) If we want to minimize Both, we must maximize P(X or Y) - subtract the biggest number possible. P(X or Y) can take a maximum value of 1 because probability cannot be more than 1. Least Probability of Both = .5 + .6 - 1 = 0.1 We can maximize 'Both' by simply putting the P(X) circle inside the P(Y) circle and hence Both = 0.5 ANSWER: Least = 10%, Greatest = 50% Here is a video that explains how max-min is done in Sets: https://youtu.be/oLKbIyb1ZrI You can check how to apply the same concepts on Probability in my content on Sunday (through Super Sundays). Details here: https://youtu.be/gN_vlDpUflo

SirSanguine · Answer

Hi Marty,

I don't think here set X and Y are part of the same sample space, hence aforementioned formulae can't be applied.

Araevin · Answer

Use a grid to solve this:

X is when X makes a profit and X’ is when it doesn’t make a profit (we don’t care if it’s a loss or breakeven). Same for Y.

~ | X | X’|
Y |....|....| 60
Y’|....|....| 40
~ |50|50|100

Here we’re asked to find min & max values for X and Y both making a profit, this is the first box in the above grid. Remember all rows and all columns have to add up to the numbers at the end of the row and column respectively. We’re given the sums of first row and first column. Logically the first row represents Y making a profit, which is made up of two scenarios of Y making a profit while X making a profit and while X not making a profit. This sum is 60%. Similar logic for all other rows and columns.

We derive the sums of the second row and second column because sum of probabilities of an event happening and not happening is 100%.

If XY’ is max then XY is min. XY’ max is 40 because XY’+X’Y’ is 40 (second row). XY’+XY is 50 (first column) => XY is 10.

Similarly if XY’ is min then XY is max. XY’ min is 0 => XY is 50.

pawanlulla · Answer

Hi

Can you please guide, how shall I learn/improve this concept? i.e. Probability and Overlapping Sets, as I have been struggling with this topic
Do you have any material/explainer video of yours on this topic? since your explanations actually help.

Thanks!

PeachSnapple1 · Answer

I swear I read and reread the prompts no fewer than 15 times and still could not get what they are asking. It turns out it was a Overlapping set problem all along.

. I was like "Huhh, why is there a range of possibility here? Isn't the probability for both companies to post a profit is just simply 50% x 60% = 30%, and of course there is no answer such as 30%." My mistake was I assumed they are independent events. Maybe I was so tired when doing this question that the possibility of an overlapping set just flew over my head. The     is a dead giveaway of an Overlapping set...

PeachSnapple1 · Answer

Found a similar question, which shares the same concept:  https://gmatclub.com/forum/rashika-is-beginning-a-new-job-in-human-resources-and-expects-to-be-425737.html

According to a prominent investment adviser, Company X has a 50% chanc

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