Question

The table above shows the probability distribution for the number of videos rented. Notice the notation of x and p(x). What is the probability that a customer rents less than three videos

Answer 1

Given the table:
x :        0 | 1 | 2    |3    | 4or more
P(x) : 0.1| ? | 0.3 | 0.2| 0.1

From the table, the probability that a customer rents no video is 0.1, the probability that a customer rents two videos is 0.3, the probability that a customer rents three videos is 0.2, the probability that a customer rents four or more videos is 0.1, the probability that a customer rents one videos is unknown.

Recall that the summation of the probabilities of all possible evens is 1.
i.e. let the probability that the customer rents one video be x, then 0.1 + x + 0.3 + 0.2 + 0.1 = 1

Thus the probability that the customer rents one video is given by 1 - (0.1 + 0.3 + 0.2 + 0.1) = 1 - 0.7 = 0.3

That a customer rents less than three videos mean that the customer rents either no video or one video or two videos.
Thus the probability that a customer rents less than three videos is given by the sum of the probabilities that the customer rents either no video or one video or two videos.

Therefore, the probability that a customer rents less than three videos = P(0) + P(1) + P(2) = 0.1 + 0.3 + 0.3 = 0.7