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If the probability that Stock A will increase in value during the next

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tann412

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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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File comment: Stock A Stock B Venn

Probability - Stock A Stock B.jpg [ 39.89 KiB | Viewed 7039 times ]

mmdfl

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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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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

sachi-in

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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

Show Spoiler

Attachment:

2017-09-08.png

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)

Rebaz

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19 May 2024, 03:48

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Raihanuddin

Please check the attachment

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!

findingmyself

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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

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Attachment:

2017-09-08.png

kanwar08

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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

RoopalKaushal

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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

hemi11984

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16 Jul 2025, 04:40

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MHIKER

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Attachment:

2017-09-08.png

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)