Question

Hhhhlllllloooooo.....! Say fast plz
From the first 50 natural numbers, find the probability of getting perfect squares and common multiples of 4..

Answer 1

ANSWER::

Natural numbers start from 1. As it is said to form 50 natural numbers, so 1 to 50 are the 50 natural numbers.

So let's see how many perfect squares are there between these;
1. 2×2 = 4.
2. 3×3 = 9.
3. 4×4 = 16.
4. 5×5 = 25.
5. 6×6 = 36.
6. 7×7 = 49.

➡So there are 6 square numbers.

Let's see multiple of 4.
1. 4×1 = 4.
2. 4×2 = 8.
3. 4×3 = 12.
4. 4×4 = 16.
5. 4×5 = 20.
6. 4×6 = 24.
7. 4×7 = 28.
8. 4×8 = 32.
9. 4×9 = 36.
10. 4×10 = 40.
11. 4×11 = 44.
12. 4×12 = 48.

➡So, 12 numbers are the common multiple of 4 in first 50 natural numbers.

But;
Some common numbers are also there which are repeated 2 times.
The numbers are :-
➡4.
➡16.
➡36.

So, let's count them as one.
So, the total number of square and multiples of 4 are 12+3 = 15.

Now the probability is;
$\frac{\large{15}}{\large{50}}$
= $\frac{\large{3}}{\large{10}}$