**Outcome: G4 **apply tree diagrams to interpret and determine probabilities

**Originator:** Stefan Schultze

**Explanation: **A tree diagram is used to show all possible possibilities of one or more dependent or independent events. It can also be used to determine the probability for a certain wanted event.

A tree diagram is so called because it looks like branches of a tree.

It shows on the top the first event and all its possible endings which can result from it.

On the second level from the top it shows all possible events on the branches which can happen after or because of the fact the first event happened.

Example:

I go to McNogood to by a sad-meal. It includes a burger, a soft drink and ice-cream.

I can choose from 2 burgers (pork and chicken) 2 __different__ soft drinks (pepsi, cola) and three different kinds of ice cream (white chocolate, black chocolate or low-fat-sugar).

To show how my final sad-meals can be combined we draw a tree diagram:

Now you could figure out by counting how many different sad-meals could be chosen (12) and how many of these would be with a Chicken burger but without Cola (3).

If you would like to know the probability of getting the low-fat-sugar-ice-cream by picking totally random (low-fat-sugar-ice-cream is the only reason you go to McNogood) you just count how many meals would involve l.f.s.i.c. (4) and divide this number by all possible Sad-Meal combinations. (12)

Example Problem:
A fair coin is tossed three times. What is the probability for:

a) no tails

b) two heads at least

c) only heads

Tree-diagram:

Possible outcome: 8

a) ways with no tail: 1

b)ways with two heads at least: 4

c) ways with only heads: 1

## Comments (1)

## Anonymous said

at 7:33 pm on Jun 14, 2007

Nice work Stefan.

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