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 most 3 people are in line at 3 pm on Friday afternoon?

May 19, 2015

At most 3 people in the line would be.

$P \left(X = 0\right) + P \left(X = 1\right) + P \left(X = 2\right) + P \left(X = 3\right)$
$= 0.1 + 0.3 + 0.4 + 0.1 = 0.9$

Thus $P \left(X \le 3\right) = 0.9$

Thus question would be easier though to use the compliment rule, as you you have one value that you are not interested in, so you can just minus it away from the total probability.

as:

$P \left(X \le 3\right) = 1 - P \left(X \ge 4\right)$
$= 1 - P \left(X = 4\right) = 1 - 0.1 = 0.9$

Thus $P \left(X \le 3\right) = 0.9$