GATE CS 2014 Set 3 — Question 58
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
Let be a sample space and two mutually exclusive events and be such that . If denotes the probability of the event, the maximum value of is ______.
Correct answer
0.25 to 0.25
Solution
Given that events and are mutually exclusive and , they form a partition of the sample space. Therefore:Let . Then .
We need to maximize the product .Let .
To find the maximum, take the derivative with respect to and set it to 0:The second derivative , which is negative, confirming a maximum.
The maximum value is:
We need to maximize the product .Let .
To find the maximum, take the derivative with respect to and set it to 0:The second derivative , which is negative, confirming a maximum.
The maximum value is:
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