Chapter 5 Supplemental Homework

Sample Spaces and Classical Probability

1. Letecia is planning a birthday for her girlfriend Scheherazade and wants everything to be perfect, but she has a few decisions
to make. First, she needs to decide which movie to take her to: Succulent Life, or Goats in Space. Second, she needs to decide
where she wants to take Sche to eat afterward: Leona’s vegan taco truck, or Hadey’s House of Hummus. Finally, she needs to
pick an outfit. She’s narrowed it down to outfit 1: button-up, tie and slacks or outfit 2: maxi dress.

a. Construct a sample space of all possible plans Letecia could come up with. I recommend a decision tree.

b. If she makes all of the choices by tossing a fair coin, what is the probability she will pick both Goats in Space for the
movie and Hadey’s House of Hummus for dinner?

2. Jupiter’s sock drawer contains 7 blue socks and 8 green socks.  Three of the blue socks have a hole in them, as does 1 of the
green socks.
a. If Jupiter pulls out one sock at random, what is the probability that it has a hole?
b. If Jupiter pulls out one sock at random, what is the probability that it is green?
c. If Jupiter pulls out one sock at random, what is the probability that it is green OR has a hole in it?

Special Multiplication Rule:

3. Sche has written a love letter to Letecia and wants to deliver it in a romantic way, such as baking it into a cake or having someone
float it downstream while they are walking by a river. The problem is, romantic approaches aren’t always practical, and Sche estimates that any of the five methods she has imagined have only a 65% chance of success. So to be safe, she decides to try all five methods. Assume that each attempt is independent of the
others.

a. What is the probability that all five attempts succeed?

b. What is the probability that all five attempts fail?

c. What is the probability that AT LEAST ONE of the attempts succeeds?

4. Letecia goes to her friend Sarkis to bake a birthday cake for Sche, and he asks if he can experiment with a few new ideas he
has. Letecia is nervous, but agrees. Sarkis wants to try an avocado cake (since he and Letecia live in Avocado Park), a durian
cake, a chili chocolate cake and a tomato cake. Letecia asks if any of them will actually taste good and Sarkis says there is about a
75% chance that they will. Even though they will all bake in the same kitchen, assume that the success or failure of each cake is independent.

a. What is the probability that all 4 cakes will taste good?

b. What is the probability that none of the 4 cakes will taste good?

c. What is the probability that AT LEAST ONE of the 4 cakes will taste good?

d. What is the probability that the chili chocolate and the avocado cakes will taste good, while the durian and the
tomato cakes will NOT?

General Multiplication Rule:

5. Jupiter realizes that she will actually need two socks for her two feet. Her sock drawer still has 7 blue socks and 8 green socks.
Apart from the holes in 3 of the blue socks and one of the green socks, the socks of each color are identical. Suppose the socks
are jumbled and it is dark in the room and Jupiter takes 2 socks out of the drawer.

a. What is the probability that both socks are blue?

b. What is the probability that both socks are green?

c. What is the probability that both socks are blue and have no holes?

d. What is the probability that both socks are green and have no holes?

e. What is the probability that Jupiter picks out a matching pair of socks with no holes in them?

6. It’s about time for the annual cupcake festival in Avocado Park and this year there are 14 varieties available. Sarkis and his
husband Ramon attend naturally, and Ramon grabs them 4 cupcakes to try at random, unaware that one of the 14 is a poison
ivy cupcake intended for goats. What is the probability that all 4 of Ramon’s selections are safe to eat?

Combinatorics:

7. The Avocado Park Development Council has a total of 70 members, including 30 humans, 18 goats, 12 dogs, 2 cats and 8
peafowl. A working committee on affordable housing is being formed and is to consist of 4 humans, 2 goats, 2 dogs a cat and a
peafowl. How many committees can be made with those conditions?

8. Hadey is hiring servers for his House of Hummus and receives applications from 17 qualified applicants, 5 of which are goats. He
has six positions available. Suppose that the species is not a factor in the hiring process.

a. What is the probability that Hadey will hire no goats at all?

b. What is the probability that Hadey will hire all 5 of the goats?

c. What is the probability that Hadey will hire exactly 4 of the goats?

d. What is the probability that Hadey will hire AT LEAST 4 of the goats?

Conditional Probability:

9. Letecia’s goats have developed a taste for spicy food. In fact, 83% of the goats enjoy spicy food. Of the goats that enjoy spicy
food, 23% have started learning a language since moving to Avocado Park. Of the goats that do not enjoy spicy food, only 12%
have started learning a new language.

a. Use a decision tree or a contingency table to find the probabilities of all 4 possible outcomes from the information described in this problem.
b. What proportion of Letecia’s goats have started learning a new language since moving to Avocado Park?
c. What proportion of the goats that have started learning a new language like spicy foods?