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tann412
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If the probability that Stock A will increase in value during the next 16 Sep 2018, 09:47
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Using Venn Diagrams is also a great way to solve such a question.
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If the probability that Stock A will increase in value during the next 24 Jun 2023, 18:11
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i illustrated what was said in the previous answers to more visual folks like me
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007saisurya
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If the probability that Stock A will increase in value during the next 11 Jul 2023, 19:51
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Answers have been complicated
a happening - .54
a not happening - .46
b happening - .68
b not happening - .32
for A not happening and B not happening to be max - find the lowest of the not happenings - 0.32
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If the probability that Stock A will increase in value during the next 24 Jan 2024, 10:14
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MHIKER
If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

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This problem can be reduced to an problem in Set making it super easy to solve.

Imagine there are 100 datasets (A, B) A is true or false depending on wheather there is a increase in A ( same for B )

there will be 54 such As with true
there will be 68 usch Bs with true

Union of A U B is set of all pairs ( A, B ) where there is a rise in both stocks.

Similarly where there is no rise = Whole Set - (Rise in A) - (Rise in B) + (Rise in both A and B)

This is maximum when the (Rise in both A and B) = (Rise in A)
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If the probability that Stock A will increase in value during the next 19 May 2024, 03:48
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Raihanuddin
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­Finally i understand this question by vissualizing it this way instead of all those long posts(which i appreciate as well).

Thank you a lot!
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If the probability that Stock A will increase in value during the next 13 Apr 2025, 06:19
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Hi All,

Another approach I have figured out for this question. Pl comment if my thought process is correct

P(A or B)= P(A)+(PB)-P(A and B)+ P(Neither)
What we want to find out is MAX value of P(neither)

P(A or B)=1
1=0.54+0.68-Both+Neither
1-0.54-0.68+Both= Neither
For Neither to be Highest, Both has to be equal to the lowest possible probability of A/B, In this case 0.54
Substituting 0.54 in the above, we get 1-0.54-0.68+0.54= 1-0.68= 0.32-->32%


MHIKER
If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

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2017-09-08.png
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kanwar08
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If the probability that Stock A will increase in value during the next 30 Jun 2025, 20:47
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This problem can be easily addressed via the Ven Diagram.

Draw two Ven Diagram for A and B. Now, my goal is to maximise the neither, which is only possible when the sets have total overlap on each other.

So, max of either will be 0.68. So, the max neither set will be 1 - 0.68 = 0.32
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If the probability that Stock A will increase in value during the next 02 Jul 2025, 03:58
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Not A = 1- 0.54 = 0.46
Not B = 1-0.68 = 0.32
Highest common probability among both = 0.32
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If the probability that Stock A will increase in value during the next 16 Jul 2025, 04:40
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MHIKER
If the probability that Stock A will increase in value during the next month is 0.54, and the probability that Stock B will increase in value during the next month is 0.68. What is the greatest value for the probability that neither of these two events will occur?

A. 0.22
B. 0.32
C. 0.37
D. 0.46
E. 0.63

Show Spoiler
Attachment:
2017-09-08.png
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Lets P(A), P(B) are the probabilities that stock A and B will increase respectively. P(A and B) is the probability that both will increase simultaneously. We know
P(A or B) = P(A) + P(B) - P(A and B)
= 0.54 +0.68 - P(A and B)
We need to determine the greatest value of probability that neither of the two stock will increase which is nothing but the greatest value of 1 - P(A or B). 1 - P(A or B) is maximum when P(A or B) is minimum. The least value of P(A or B) will be when P(A and B) = P(A). therefore least value of P(A or B) = 0.68. Finally, the greatest value of probability that neither of the two stock will increase is 1-0.68 = 0.32. Ans (B)
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If the probability that Stock A will increase in value during the next 27 Jul 2025, 20:25
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If the probability that Stock A will increase in value during the next 06 Oct 2025, 00:06
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If the concepts are clear, then I guess this the good to go approach
Raihanuddin
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If the probability that Stock A will increase in value during the next 25 Jun 2026, 02:50
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750-scorer approach
Let:
(A) = Stock A increases, P(A)=0.54
(B) = Stock B increases, P(B)=0.68
We want the greatest probability that neither increases:
P(neither) = 1 - P(A ∪ B)
So we want to make P(A ∪ B) as small as possible.
-------------------------------------------------

Key idea
To minimize the union, make the two events overlap as much as possible.
Maximum overlap:
P(A ∩ B) = min(0.54, 0.68) = 0.54
Then,
P(A ∪ B) = 0.54 + 0.68 - 0.54 = 0.68
Therefore,
P(neither) = 1 - 0.68 = 0.32
----------------------------

Answer
0.32
Choice B
--------

5-second GMAT shortcut
For two events with probabilities (a) and (b):
Maximum probability of neither = 1 - max(a, b)
because the events can completely overlap.
So:
1 - 0.68 = 0.32
Done.
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