Question

# People visiting video rental stores often rent more than one DVD at a time. The probability...

People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given in the table below. There is a five-video limit per customer at this store, so nobody ever rents more than five DVDs.

x P(x)
0 0.04
1 0.47
2 0.24
3
4 0.08
5 0.04

Find the probability that a customer rents three DVDs. (Enter an exact number as an integer, fraction, or decimal.)

Find the probability that a customer rents at least four DVDs. (Enter an exact number as an integer, fraction, or decimal.)

Find the probability that a customer rents at most two DVDs. (Enter an exact number as an integer, fraction, or decimal.)

Solution:
Given in the question
Probability distribution is given and Total probability of probability distribution is 1
Solution(a)
We need to calculate the probability that a customer rents three DVDs which can be calculated as
P(X=3) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=4) - P(X=5) = 1- 0.04-0.47-0.24-0.08-0.04 = 1-0.87 =0.13
Solution(b)
We need to calculate the probability that a customer rents at least four DVDs
P(X>=4) = P(X=4) + P(X=5) = 0.08 + 0.04 = 0.12
So there is 12% probability that a customer rents at least four DVDs
Solution(c)
We need to calculate the probability that a customer rents at most two DVDs
P(X<=2) = P(X=0) + P(X=1) + P(X=2) = 0.04 + 0.47 + 0.24 = 0.75
So there is 75% probability that a customer rents at most two DVDs.

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