Question

A survey of Amazon.com shoppers reveals the following probability distribution of the number of books purchased per hit.

X 0 1 2 3 4 5 6 7

P(X) .35 .25 .20 .08 .06 .03 .02 .01

a. What is the probability that an Amazon.com visitor will buy four books?
b. What is the probability that an Amazon.com visitor will buy eight books?
c. What is the probability that an Amazon.com visitor will not buy any books?
d. What is the probability that an Amazon.com visitor will buy at least one book?

Answer 1

a)
`P(X=4) = 0.06`

b)
`P(X=8) = 0`

c)
`P(X=0) = 0.35`

d)
`P(X\geq 1)= 1-P(X<1) = 1-P(X=0) = 1-0.35 =0.65`

Explanation:

For this case we define the random variable X as "number of books purchased per hit."

And as we can see the distribution for x is given by:

X 0 1 2 3 4 5 6 7

P(X) .35 .25 .20 .08 .06 .03 .02 .01

Part a

For this case we want this probability:

`P(X=4) = 0.06` from the probability distribution given

Part b

For this case we want this probability:

`P(X=8) = 0` from the probability distribution given since the value of X=8 is not in the distribution

Part c

For this case we want this probability:

`P(X=0) = 0.35` from the probability distribution given

Part d

For this case we want this probability:

`P(X\geq 1)`

And we can use the complement rule like this:

`P(X\geq 1)= 1-P(X<1) = 1-P(X=0) = 1-0.35 =0.65`