# You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the probability that at least 3 people are in line at 3 pm on Friday afternoon?

Jan 2, 2015

This is an EITHER... OR situation. You may ADD the probabilities.

The conditions are exclusive , that is: you can't have 3 AND 4 people in a line. There are EITHER 3 people OR 4 people in line.

So add: $P \left(3 \mathmr{and} 4\right) = P \left(3\right) + P \left(4\right) = 0.1 + 0.1 = 0.2$

$P \left(< 3\right) = P \left(0\right) + P \left(1\right) + P \left(2\right) = 0.1 + 0.3 + 0.4 = 0.8$
And this and your answer add up to $1.0$, as they should.