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Question

The sum of two +ve quantities is equal to 2n. The probability that their product is not less than 34 times their largest product is

A
34
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B
14
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C
23
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D
12
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Solution

The correct option is C 12
Let one of the number (quantity)be x.So the other is 2n-x.
Now product of x and 2n-x will be largest if these two numbers are equal
2nx=x
x=n
both are equal to n so product =n2
Now by problem x(2nx)34× their product
Note n(S)=2n x(2nx)34n2
4x28nx+3n20 n2x32n
Now n(A)=3n2n2=n
P(A)=n(A)n(S)=n2n=12

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