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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

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)
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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!
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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

Attachment:
2017-09-08.png
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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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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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