Find the probability of a number which is divisible by either 5 or 3 o...
The First 500 Natural Odd numbers are given as 1,3,5,7,…………….999.
The Numbers divisible by 3 from the above list are given as 3,9,15,21…………999
The above series is in Arithmetic progression,
Tn = a+(n−1)d
999 = 3+(n3−1)6 ⇒ n3 = 167
So total Numbers which are divisible by 3 in the given list is, n3 = 167
The Numbers divisible by 5 from the above list are given as 55,15,25,35…………99
The above series is in Arithmetic progression,
Tn = a+(n−1)d
995 = 5+(n5−1)10 ⇒ n5 = 100
So total Numbers which are divisible by 5 in the given list is, n3 = 100.
The Numbers divisible by 15 from the above list are given as 15,45,75,105…………975
The above series is in Arithmetic progression,
Tn = a+(n−1)d
975 = 15+(n15−1)30 ⇒ n15 = 33
So total Numbers which are divisible by 3 in the given list is, n3 = 33
So Required Probability p = p(n
3)+p(n
5)−p(n
15) =
= 0.468