A natural number x is chosen at random from the first 100 natural numbers. Then the probability that, x+100x>50 is:
A
120
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B
1120
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C
13
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D
None
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Solution
The correct option is B1120 x+100x>50⇒x2−50x+100>0,1≤x≤100,x∈Z. ⇒1≤x<25−5√21 or 25+5√21<x≤100 ⇒x=1,2,48,49,......,100. ∴ Total number of ways = 100,
and favourable ways = 55.. ∴ Required probability =55100=1120