Project #57158 - probability

 

At ACME alarms, the company has developed three different types of wireless home alarm systems: Model X100 (aka Model “X”), Model Y200 (aka Model “Y”) and Model Z300 (aka Model “Z”). One day on the assembly line, the boxes used to package the system were not labeled, i.e., they were all packed into plain, unmarked boxes of the same size and shape, and therefore, by just looking at the box, you couldn't tell whether it contained Model X100, Model Y200 or the Model Z300. It's not until you actually open the box that you can tell which model was packed inside of it. On this day, hundreds of such boxes were packaged and loaded into a truck. We don't know the exact number; the only thing we know for sure is that an equal number of Model X100's, Model Y200's and Model Z300's were packed into the truck. The plant manager asks you to pick three boxes out of the truck at random and place them in bins labeled “A,” “B” and “C.” That is, something like this:

 

 

 

First box selected Second box selected Third box selected

 

A             B                C

 

 

 

2. Let E = the event that all three bins contain the same model. Then P(E) = _______/__________.

 

3. What is the probability that bin “B” will contain the Model Z300?

 

Let E = Bin B contains the Model Z300.

 

Then, the desired number of outcomes is ________ and the total possible outcomes is _________ making P(E) = ______/________.

 

4. What is the probability that bin “A” and bin “C” will contain the same model?

 

Let E = Event that bin "A" and bin "C" contain the same model.

 

Then the number of desired outcomes is ______ and the total number of possible outcomes is _______ making P(E) = _______/_______

 

5. What is the probability that all three bins will contain different models?

 

Let E = the event that all three bins will contain different models.

 

Then, the number of desired outcomes is ________ and the total number of possible outcomes is_________ making P(E) = ________/________.

 

6. What is the probability that two bins will contain the same model and the other a different model?

 

Let E = the event that two bins will contain the same model and the other bin contains a different model than the other two (which are the same).

 

Thus, the number of desired outcomes is ________ and the total number of possible outcomes is _______ make P(E) = ______/_______.

 

7. What is the probability that bin “B” will contain the Model Y200?

 

Let E = the event that bin "B" will contain the Model Y200?

 

Then, the number of desired outcomes is _______ and the total number of possible outcomes is _______ making P(E) = ______/_________.

 

 

 

8. Using the sample space for two dice on page 216 of your text book, what is the probability of throwing “Outside Numbers” - the numbers 4, 5, 9, and 10 in the game of craps? We assume, of course, we’re throwing two fair dice.

 

  A.

 

14/36

 

 

 

  B.

 

4/36

 

 

 

  C.

 

4/6

 

 

 

  D.

 

4/12

 

   E.

 

None of these options are correct

 

 

 

9.

 

 

 

Use the sample space for two dice on page 216 of your text book, what is the probability of winning a “Field Bet” - A bet on 2, 3, 4, 9, 10, 11 or 12 in the game of craps? We assume, of course, we’re throwing two fair dice.

 

 

 

 

 

  A.

 

16/36

 

 

 

  B.

 

7/36

 

 

 

  C.

 

7/12

 

 

 

  D.

 

5/12

 

 

 

  E.

 

None of these options are correct

 

 

 

If you place the boxes in the bins as described, how many possible outcomes could there be when you open the boxes? For example, one outcome could be that in bin A we had the model X100, in bin B we had the model Y200 and in bin C we had the model Z300. This outcome could be written in shorthand (by using the short-name for each model) as XYZ.

 

  1. 9        b.27          c.12      d.  3

 

Subject Mathematics
Due By (Pacific Time) 02/11/2015 12:00 am
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