Tag Archives: probability

23. Coffee overload

I was sat in a coffee shop when I overheard the barista say to a customer ‘Take your time, there are about 20,000 different drinks available’.

Sounded like a mathematical challenge to me.

image

If the menu below was real, how many different drinks could made?

How many would be drinkable?

Size: S, M, L

Drink: Filter, Americano, Cappucinno, Machiatto, Latte, Espresso, Hot chocolate.

Coffee type: Decaf or caffeinated

Flavour: Vanilla, Mint, Hazelnut, Ginger, Caramel, None

Milk: None, whole, skimmed, soya

Hint: Be methodical, work out the hot chocolate options first.

Solution
Hot choc
Size *Flavour*Milk = 3*6*4 = 72

Coffee
Size*Drink*Type*Flavour*Milk =
3*6*2*6*4 = 864

Total number of drinks
864 + 72 = 936

This doesn’t consider extra shots of coffee or syrup. Imagine how many variations there are in a big coffee shop!

Me … I’ll have a black filter, no milk, no sugar.

14. JDs Tree Diagram

My friend JD came up with this visual way of explaining tree diagrams. I’m reproducing it here with permission (Thanks!). It helps if you have a school uniform with a tie and jumper, however this could easily be done with coats and hats.

Set Up
You need 6 volunteers, dressed as listed:
1. (No jumper, no tie) x 2
2. (No jumper, tie) x 2
3. Jumper, tie
4. Jumper, no tie

(This can be adapted for listing multiple outcomes too)

Activity
Draw a V shape on the ground.
Explain that in the morning you have choices when you get dressed. Each branch represents a choice.
Choice 1: Do you put your tie on or not?
Get a student wearing a tie to stand at the end of one branch and one without a tie to stand at the end of the other

Draw a V from each student.
Choice 2: Do you put your jumper on or not?
Get the class to decide who stands where

Discussion
If all the choices are equally likely, what is the probability of getting in trouble with your teacher over uniform?
Can you prove this by looking at the probabilities of the individual events?
What would happen if the outcomes were not equally likely?

It’s a good idea to try and take a picture of what this looks like to display in class. You could also annotate it with fractions and overall probabilities.