Question

1.
Find a number x is selected from natural numbers 1 to 100, find the probability
100
for x+
> 29​

Answer 1

Answer:

x+x100>50⟹x2+100>50x⟹x2−50x+100+(25)2−(25)2>0⟹x2+(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, =10055