if a number x is selected from the number 1to100 then the probability for x + 100/x > 29
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A number x is selected from first 100 natural numbers. Find the probability that x satisfies the condition x+
x
100
>50
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x+
x
100
>50
⟹x
2
+100>50x
⟹x
2
−50x+100+(25)
2
−(25)
2
>0
⟹x
2
+(25)
2
−50x−525>0
⟹(x−25)
2
>525
⟹x−25>±
525
⟹x>25+22.91,x<25−22.91
⟹x>47.91,x<2.09
⟹x≥48,x≤2
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, =
100
55
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