Calculating Shoe Sales Probabilities: A Workbook Exercise

[bnosam]

Homework Statement

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 0.6Probability of purchasing Blue shoes?
Probability of Red or Green?
Probability of Red or Blue?
Probability of Blue or Green?
Probability of not buying anything?

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

Any suggestions?

 

[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.

 

[bnosam]

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

 

[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%.

 

[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.

 

[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.

 

[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.

 

[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.

 

[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) + [edit] P( X and Y and Z) .

 

[bnosam]

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) + 2P( X and Y and Z) .

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.

 

[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).

 

[bnosam]

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

 

[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).

 

[bnosam]

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

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

 

[Ray Vickson]

Homework Statement

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 0.6Probability of purchasing Blue shoes?
Probability of Red or Green?
Probability of Red or Blue?
Probability of Blue or Green?
Probability of not buying anything?

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

Any suggestions?

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.