Statistics 325 Assignment 4 Spring 2023
Be sure to justify your answers.
1. In a certain locality, 50% of all adults regularly consume coffee, 60% regularly consume
carbonated soda, and 10% regularly consume neither coffee nor carbonated soda. If we
select an adult at random from this locality, then
P(the selected adult regularly consumes coffee) = .50,
P(the selected adult regularly consumes carbonated soda) = .60, and
P(the selected adult regularly consumes neither of these products) = .10.
Let Adenote the event “regularly consume coffee” and let Bdenote the event “regularly
consume carbonated soda”. Express each of the following events in terms of Aand Band
compute its probability.
a) A randomly selected adult regularly consumes both coffee and soda.
b) A randomly selected adult regularly at least one of these two products.
c) A randomly selected adult consumes coffee but not carbonated soda.
d) A randomly selected adult regularly consumes one of these two products but not both.
2. A customer visiting the suit department of a certain store will purchase a suit with
probability .22, a shirt with probability .30, and a tie with probability .28. The customer
will purchase both a suit and a shirt with probability .11, both a suit and a tie with
probability .14, and both a shirt and a tie with probability .10. A customer will purchase
all 3 items with probability .06.
Hint: Let Adenote the event “purchase a suit”, Bthe event “purchase a shirt”, and C
the event “purchase a tie”. Create (or use the one provided) a Venn diagram showing the
partition of A∪B∪Cinto seven disjoint regions along with the complementary region,
determine the proportion of customers in each of these eight regions, and add these numbers
to your Venn Diagram.
a) What is the probability that a customer purchases at least one of these items?
b) What is the probability that a customer purchases none of these items?
c) What is the probability that a customer purchases exactly one of these items?
d) What is the probability that a customer purchases all three of these items?
