Question

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.)

Answer #1

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.

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
0.03
1
0.54
2
0.24
3
4
0.06
5
0.04
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