Question

The probability that a person chosen at random is left handed (in hand writing) is $0.1$. What is the probability that in a group of $10$ people, there is one who is left handed?

Answer 1

The probability of a person chosen at random being left handed is $0.1$

In a group of ten people, if we need one person who is left handed, first we choose that person in ten ways.

Next, we multiply by the probability of being a left handed and the probability of the other persons being right handed.

This turns out to be ${}^{10}{C}_1\times (0.1{)}^1\times (1-0.1{)}^9$

$=(0.9{)}^9$

$=0.387$