# Shoe Sales Probability

1. Feb 1, 2015

### bnosam

1. The problem statement, all variables and given/known data

A question out of my a workbook I have:

We have sales from a shoe store:

Probability of Red Shoes 0.35
Probability of Green Shoes 0.40
Probability of Red, Green, Blue Shoes 0.05
Probability of Red and Green Shoes 0.1
Probability of Green and Blue Shoes 0.2
Probability of Red and Blue Shoes 0.25
Probability of Red or Blue Shoes 0.6

Probability of Red or Green?
Probability of Red or Blue?
Probability of Blue or Green?

I'm not sure how to do probabilities in this format really?

Any suggestions?

Last edited: Feb 1, 2015
2. Feb 1, 2015

### RUber

Draw a box diagram. The total area of the box should be 100%. Red will have an area of .35, Green will have an area of .40. Blue = ??. Other areas should be intersections of the areas.

3. Feb 1, 2015

### bnosam

Sorry, this is my first prob-stats class. What is a box diagram?

4. Feb 1, 2015

### RUber

Draw a big box, and start breaking it into regions that have certain areas.
The biggest challenge here is ensuring that everything adds up to 100%.

5. Feb 1, 2015

### RUber

Remember that red, green, and blue = .05 means that 5% of the 100% should be in all three areas.
Red and Blue also includes that 5% that is in red, blue and green, so sometimes it is easier to count up from the greatest intersection.

6. Feb 1, 2015

### bnosam

Oh ok, I broke it up into a Venn diagram earlier, but I don't quite get values from it because I need to know the number of people who didn't buy and the number of people who bought blue.

7. Feb 1, 2015

### RUber

The total number is 100%, you should be able to find the area for blue by using some of the other relations.
Think of all the possible combinations of blue and look at your probability of red or blue. You are given everything but blue alone.

8. Feb 1, 2015

### bnosam

So it doesn't make a difference that we have two unknowns? People who didn't buy and people who bought blue?

Sorry if I seem dense. This stuff is confusing to me, I just can't comprehend it well at all. I found Calc 1 through 3 to be fine, but this stuff. I have no idea why.

9. Feb 1, 2015

### RUber

You have a lot more knowns that unknowns. Just piece them all together.
Remember that P(X or Y) = P(X)+P(Y) - P(X and Y).
Similarly, P(X or Y or Z) = P(X) + P(Y) + P(Z) - P(X and Y) - P(X and Z) - P(Y and Z) +  P( X and Y and Z) .

Last edited: Feb 1, 2015
10. Feb 1, 2015

### bnosam

Is there a table where I can find these online somewhere? They're not in my book and wasn't shown them in class.

P(Red or Blue) = P(Red) + P(Blue) - P(Red and Blue)
.6 = .35 + P(BLUE) - .25

P(Blue) = .5? That can't be right.

Last edited: Feb 1, 2015
11. Feb 1, 2015

### RUber

Why not? Remember, most of the numbers given are overlapping regions. As you build your Venn diagram, you should be able to determine what the P(Blue and not red and not green), P(Blue and Green and not red), P(Blue and Red and not green), and P(Blue and Green and Red). These would be mutually exclusive areas which would add up to P(Blue).

12. Feb 1, 2015

### bnosam

I guess I was thinking Red + Blue + Green has to be 1.0 when added but that's not true.

13. Feb 1, 2015

### RUber

I edited post #9. Use that to find out the probability that nothing is bought. i.e. 1 - P(Red or Blue or Green).

14. Feb 1, 2015

### bnosam

Ah ok I figured this out now. Thank you for your help :)

15. Feb 1, 2015

### Ray Vickson

Draw a Venn diagram; see, eg.,
http://www.mathsisfun.com/sets/venn-diagrams.html
http://mathworld.wolfram.com/VennDiagram.html

Remember also: "or" is an 'inclusive or', meaning "and/or", so those who buy "red or green" may buy (i) red alone, (ii) green alone, or (iii) both red and green.