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Question

A number x is selected from first 100 natural numbers. Find the probability that x satisfies the condition x+100x>50

A
55100
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B
45100
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C
1
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D
50100
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Solution

The correct option is B 55100
x+100x>50x2+100>50xx250x+100+(25)2(25)2>0x2+(25)250x525>0(x25)2>525x25>±525x>25+22.91,x<2522.91x>47.91,x<2.09x48,x2
As we have to select from 1 to 100 and x is greater than or equal to 48. Hence we have to select from 49 to 100 which is 53 numbers and favorable cases are 1, 2.
Total favorable case = 53+2=55.
Total number of cases = 100
Hence the required probability, =55100

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