Question

A box contains 50 balls, numbered from 1 to 50. If three balls are drawn at random with replacement. What is the probability that sum of the numbers are odd?

Answer 1

There are $25$ odd and $25$ even numbers from $1$ to $50.$

Sum will be odd if$=$ odd $+$ odd $+$ odd,

odd $+$ even$+$ even,

even$+$odd $+$ even,

even$+$ even$+$ odd

$\therefore P=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}+\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{4}{8}=\frac{1}{2}$