Heads-Up Probability

I was walking through a park one day,
In the merry, merry month of ,
When much to my surprise,
Before my very ...
	*Click on the arrow to choose your answer.*

What a minute! I see something shiny on the ground. What is it?
Click on a button to make a prediction about what it is.


Click on the picture to check your answer.
	a rock
	a coin
	a bottle top
	gold

Aha! It's a coin. Before I look, do you think the coin is heads up or tails up?

Go ahead, make a prediction.

Type your prediction in the box.

Why did you predict heads or tails? Which do you think is more or less likely than the other?

Heads is more likely than tails.
Tails is more likely than heads.
Heads and tails are equally likely.

Click on the button, then click on the picture to check your answer.

One way mathematicians show what is likely or possibilities is to draw tree diagrams. Which of these pictures is a tree diagram that a mathematician might use?

Click on the button to show your answer, then click on the picture to check your answer.

A tree diagram has branches, just like a real tree.
But on a real tree diagram, the branches show what is likely or the possible outcomes of an event.

Look at the tree diagram for our problem,

What are the possible outcomes?

What is the event?

PE01165_.WMF (3994 bytes)

Of course, what is possible is that the coin is either

'heads up'
or
'tails up.'

But which is more likely, 'heads up' or 'tails up'? Or is 'heads up' or 'tails up' equally likely?

Let's conduct a mathematical experiment to see the possibilities.

	What experiment would you conduct to find out if heads or tails is more or less likely? Type your idea in the box.

	So, the tree diagram shows the possible outcomes of this event.
Our experiment will be the simple event of tossing a coin.

If the coin is tossed twenty times,
how many times do you predict the coin will land on heads?
How many times do you predict the coin will land on tails?

I tossed a coin twenty times and here is what I got.
Click in the check boxes to complete the graph. Click on the picture of the pennies to check your graph.
Which outcome was more likely, or had a greater number of outcomes, for this experiment?

Coin Toss Graph

Number of Outcomes









	Heads	Tails

What would happen if
we tossed the coin twenty more times?
Will the outcome of the experiment be more heads or tails?

Click in the check boxes to complete the Coin Toss Tally.
Click on the picture of the pennies to check your graph.
Which outcome was more likely in this experiment?

Coin Toss Graph
N U M B E R of O U T C O M E S










	Heads	Tails

What would happen if we tossed the coin twenty more times?
Will the outcome of the experiment be more heads...more tails...
or an equal number of heads and tails?

Click in the check boxes to complete the Coin Toss Tally.
Click on the picture of the pennies to check your graph.
Which outcome was more likely in this experiment?

Coin Toss Graph
N U M B E R of O U T C O M E S









	Heads	Tails

Tails was more likely in the first experiment. Heads was more likely in our second experiment. *Tails and heads were equally likely in our third.*
We need to do many more experiments to determine if... heads or tails are more likely OR to see if heads or tails are equally likely.
Now it's your turn. Use a tally sheet and toss a coin twenty more times. Record what happens or the result of the experiment. What do you think will be the outcome...
	heads or *tails*?

Oh, by the way,
the coin I found
in the park was
heads up. I guess
that means I'll
have good luck!