At Cal’s Computer Warehouse, Cal wants to know the probability that a customer who comes into his store will buy a computer or a printer.  He collected the following data during a recent week:  233 customers visited the store, 126 purchased computers, 44 purchased printers, and 93 made no purchase.

a)  Draw a Venn diagram:

 

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.

1. 1. Determine the expected number of customer arrivals for a five-minute period. (hint: this is   )
   2. If X = the number of arrivals per minute:
      Find the probability of 10 customers or less arriving within a minute.
   3. Find the probability of more than 7 customers arriving within a minute. 
   4. Find the probability of 3 customers arriving within a minute. 

Let X denote the number of Canon digital cameras sold during
a particular week by a certain store. The pmf of X is
x | 0 1 2 3 4
pX(x) | .1 .2 .3 .25 .15
Sixty percent of all customers who purchase these cameras
also buy an extended warranty. Let Y denote the number of
purchasers during this week who buy an extended warranty.

a. What is P(X =4, Y = 2)? [Hint: This probability equals
P(Y = 2 I X = 4) * P(X = 4); now think of the four purchases
as four trials of a binomial experiment, with success
on a trial corresponding to buying an extended warranty.]
b. Calculate P(X = Y).
c. Determine the joint pmf of X and Y and then the marginal
pmf of Y.

A local market sells avocados. Suppose there are 64 for sale and, unknown to you, 24 of them are rotten. If you were to purchase 4 avocados, chosen randomly from those available, let X denote the number of the purchased avocados that are rotten. What is the distribution of X? What is the probability that none of those purchased are rotten?