Directions: For all the problems, read the problem to decide if it is binomial (B) or geometric (G). Put the letter to the left of the problem number, then answer each question.

Question 1: Read the problem and answer all parts to it below:

Bags of plain M&M's contain 30% brown candies. One candy is selected from each of 12 bags. The random variable represents the number of brown candies selected. Find the probability that

Part A: You select 4 brown candies

Part B: You select at least 4 brown candies.

Part C: You select at most 7 brown candies.

Part D: How many brown candies to you expect to get?

Question 2: Read the problem and answer all parts to it below:

Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail pre-sale testing. The random variable represents the number of chip tested that is rejected first.

Part A: What's the probability that the fifth chip you test is the first rejected?

Part B: What's the probability that you reject a chip within the first ten you encounter?

Part C: How many do you expect to test before finding a bad one?

Question 3: Read the problem and answer all parts to it below:

A federal report finds that lie detector tests given to truthful people have probability about 0.2 of suggesting that the person is deceptive. A company asks 12 job applicants about thefts from previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully.

Part A: What is the probability that the lie detector says all 12 are truthful?

Part B: What is the probability that the lie detector says at least 1 is deceptive?

Question 4: Read the problem and answer all parts to it below:

A wildlife biologist examines frogs for a genetic trait he suspects may be linked to industrial toxins in the environment. Previous research established this trait is found in one of every eight frogs. Assume the frequency of the trait has not changed and he plans to simply test frogs as he finds them.

Part A: What is the probability he does not find the trait until the 6th frog he tests?

Part B: What is the probability he does not find the trait in the first four frogs tested?

Question 5: Read the problem and answer all parts to it below:

Assume that 13% of people are left-handed.

Part A: Imagine you select 12 people at random. What is the probability that there are less than three left-handed people in the group?

Part B: Imagine you select 25 people at random. How many left-handed people do you expect to have in the group?

Part C: Imagine you select people at random until you find a left-handed person. What is the probability that you have to ask 10 people or less?

Question 6: Read the problem and answer all parts to it below:

About 8% of elementary students at Oakview have food allergies.

Part A: If you start checking student files at random, what is the probability the fifth student file is the first to show food allergies?

Part B: About how many student files do you expect to check before finding the first one that shows food allergies?

Part C: Imagine you pulled 100 student files. What is the probability that at least 12 show food allergies?