# M650-4

**Each student is expected to post at least twice. For your original post, please select one probability problem to work on. Reply to at least one class member’s post. Replies should be meaningful. Avoid responses such as “Great job”, “I agree with you”, etc., that do not add content.**

**SAMPLE SPACES**

1. **A Girl Named Florida**

Here’s a three-part puzzler. For each part list the sample space. Listing the sample space will make the probability clear. You can denote Boy as B, Girl as G, and Florida as F when listing a sample space. For example, the sample space of the birth events boy-girl and girl-girl is {BG, GG}.

- Your friend has two children. What is the probability that both are girls?
- Your friend has two children. You know for a fact that at least one of them is a girl. What is the probability that the other one is a girl?
- Your friend has three children. One is a girl named Florida and one is a girl named Holley. What is the probability that the first child is a boy?

2. **A Game Show**

Let’s say you are a contestant on a game show. The host of the show presents you with a choice of 4 doors, which we will call doors 1, 2, 3, and 4. You do not know what is behind each door, but you do know that a new Cadillac Escalade and 3 old cars are randomly placed behind the doors. The host knows where the Escalade is. The game is played out is as follows. The host lets you choose a door. The host opens a door with an old car and asks you whether or not you want to change your door choice.

- Visualization is a powerful tool. Download the 4-Door Game Show Worksheet Worksheet (<-- Click it).
- Fill in the empty text boxes with Escalade or Old Car as determined by the sample spaces contestant keeps or switches doors.
- Complete the calculation P(Win | Switch door) and P(Win | Keep door) by revising “?” to the number of favorable outcomes.
- Attach your completed worksheet to your post.
- Should the contestant switch doors?

**PROBABILITY**

3. **A Birthday Problem**

There are 30 people in this class.

a) What is the probability that at least 2 of the people in the class share the same birthday?

b) If P(at least 2 of the people in the class share the same birthday) = 25%, how many people are in the class?

4. **Addition Rules and Real Estate**

You are a realtor. In your area there are 50 starter homes, 75 mid value homes without solar power, 15 mid value homes with solar power, 35 high value homes without solar power, and 25 high value homes with solar power. If a home is picked randomly to show

a) What is the probability it has solar power and it is a mid-value home?

b) What is the probability it has solar power or it is a mid-value home?

c) What is the probability it has not solar power and not a mid-value home?

**CONDITIONAL PROBABILITY**

5. **Disease Testing, True and False Positives**

0.05% of adults over the age of 60 have lung cancer, 95% of adults who have lung cancer will test positive (the accuracy of the test for people with the disease), and 90% percent of adults that do NOT have lung cancer will test negative (accuracy of the test for people without the disease).

a) Compute the probability of having disease and testing positive (true positive)

b) Compute the probability of not having disease and testing positive (false positive).

c) Compute P(positive test).

d) Compute P(disease | test positive).

e) If somebody tests positive for that disease, is there a 99% chance that they have the disease?

6. **Real Estate**

You are a realtor. In your area there are 50 starter homes, 75 mid value homes without solar power, 15 mid value homes with solar power, 35 high value homes without solar power, and 25 high value homes with solar power. If a home is picked randomly to show,

Using the data, make your own conditional probability problem.

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