Question

A natural number x is chosen at random from the first 100 natural numbers . find the probability that x+(100/x) > 50

Answer 1

Answer:

ANSWER

Step-by-step explanation:

Given x+

x

100

>50⇒x

2

−50x+100>0

⇒(x−25)

2

>525⇒x−25<−

525

or x−25>

525

⇒x<25−

525

or x>25+

525

As x is a positive integer and

525

=22.91, we must have x≤2 or x≥48

Let E be the event for favorable cases and S be the sample space.

∴E={1,2,48,49,50,...100}

n(E)=55 and n(s)=100

Hence the required probability

P(E)=

n(s)

n(E)

=

100

55

=

20

11

by comparing it with

20

10+k

we get 10+k=11

∴k=1