How Likely Is That?
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Shelly Berman shelly@mathforum.org

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Probability Experiments

Experiment 1

If you toss a single number cube (one die), what is the probability of rolling an even number?

One way of thinking about probability is to make a fraction that shows:

• How many different numbers could you get when you roll a number cube?
• How many of these are even?

When you roll a number cube you can get any of the six numbers: 1, 2, 3, 4, 5, or 6.

Three of these numbers are even: 2, 4, and 6.

That is, the probability of rolling an even number can be written as: P(even number) = (3 numbers we want)/(6 possible numbers) = (3/6).

So, the probability of rolling an even number on a number cube is (3/6).

• Where is this on the probability scale from 0 to 1? How do you know?

Experiment 2

How do you think we could measure the probability of tossing a die and getting a 1?

• Is it more likely that you will get a 1 or that you won't get a 1?
• In fact, can you measure the probability of tossing a die and getting any number but a 1?

Here's a set of twenty cards. Each card has a number from 1 to 10, and the number is either red or black.

If I draw one card without looking, what is the probability that the card I draw will:

• be red?

• show an even number?

• show a number less than 3?

• show a black 7?

Can you think another outcome from drawing one card that has a probability of:

• (1/2)?

• (1/4)?

• (4/20)?

• (1/20)?

• (19/20)?