MATH 314 Homework 06

1. Consider the following table giving counts for the types of each coffee purchased at my favorite coffee shop within a weekend.

   	Small	Medium	Large
   regular	19	23	22
   decaf	20	15	17

   Based on these data,
   1. what is the probability of someone ordering a regular coffee?
   2. what is the probability of someone ordering a medium coffee?
   3. what is the probability of someone ordering a large decaf coffee?
   4. what is the probability of someone ordering a small regular coffee?
   5. what is the probability of someone ordering a a regular coffee, given that they ordered a small?
   6. what is the probability of someone ordering a a small coffee, given that they ordered a regular?
   7. what is the probability of someone ordering a a large coffee, given that they ordered a decaf?
   8. is ordering a medium coffee independent of ordering a decaf coffee?
2. In a factory, two machines, A and B, are used to produce a specific part. Machine A produces 70% of the parts, and Machine B produces the remaining 30%. However, 5% of the parts from Machine A and 3% of the parts from Machine B are defective. An inspector randomly selects a part and finds it to be defective.
   1. What is the probability that this defective part was produced by Machine A?
   2. If another part is randomly selected and it's not defective, what is the probability that it was produced by Machine B?
3. Let's guess that 80% of all e-mail is spam, and the phrase "free money" is used in 10% of spam e-mails. Suppose the phrase is also used in 1% of non-spam e-mails. A new e-mail has just arrived which contains the phrase "free money". What is the probability that it is spam?