Question

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A) 1/6 B) 1/3 C) 1/2 D) 1/4

Answer 1

Correct Question:

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A) 1/6 B) 1/3 C) 1/2 D) 1/4

Answer:

$\frac{1}{2}$

Solution :

p (odd) = p (even) = 1/2 ; (because there are 50 odd and 50 even numbers)

As we know, Sum or the three numbers can be odd only under the following 4 scenarios.

$odd + odd + odd + odd = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \frac{1}{8}$

$odd + even + even \: = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \frac{1}{8}$

$even + odd + even = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \frac{1}{8}$

$even + even + odd \: = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \frac{1}{8}$

If you try solving these question by you're method you will also get all the even numbers.

Adding up the 4 scenarios above:

$\frac{1}{8} \: \: \frac{1}{8} \: \: \frac{1}{8} \: \: \frac{1}{8} = \frac{4}{8} = \frac{1}{2}$

Hence, 1/2 is the correct answer

☆Additional Information ☆

Odd numbers - Any integer or number which can't be divisible by 2 is known as odd numbers.

Even Numbers - Any integer or number that can be exactly divisible by 2 is know as even numbers.

Thanks!