# probability

Solve the following exercises:

Question 1. The Web site for M&M candies claimed that 24% of plain M&M candies are blue, 20% are orange, 16% green, 14% yellow, and 13% each red and brown.

(a) Pick one M&M at random from a package.

1. Describe the sample space.
2. What is the probability that the one you pick is blue or red?
3. What is the probability that the one you pick is not green?

(b) You pick three M&M’s in a row randomly from three separate packages.

1. Describe the sample space for the outcomes of your three choices.
2. What is the probability that every M&M is blue?
3. What is the probability that the third M&M is red?
4. What is the probability that at least one is blue?

Question 2. A survey found that 62% of callers in the United States complain about the service they receive from a call center if they suspect that the agent who handled the call is foreign.11 Given this context, what is the probability that (state your assumptions)

(a) the next three consecutive callers complain about the service provided by a foreign agent?

(b) the next two calls produce a complaint, but not the third?

(c) two out of the next three calls produce a complaint?

(d) none of the next 10 calls produces a complaint?

Question 3. A shipment of assembly parts from a vendor offering inexpensive parts is used in a manufacturing plant. The box of 12 parts contains 5 that are defective and will not fit during assembly. A worker picks parts one at a time and attempts to install them. Find the probability of each outcome.

(a) The first two chosen are both good.

(b) At least one of the first three is good.

(c) The first four picked are all good.

(d) The worker has to pick five parts to find one that is good.

Question 4. After assembling an order for 12 computer systems, the assembler noticed that an electronic component that was to have been installed was left over. The assembler then checked the 12 systems in order to find the system missing the component. Assume that he checks them in a random order.

(a) What is the probability that the first system the assembler checks is the system that is missing the component?

(b) What is the probability that the second system the assembler checks is missing the component, assuming that the first system he checked was OK?

(c) Explain why the answers to parts (a) and (b) are different.