Experimental Probability

Lesson Plan - Get It!

Audio:

When we talk about probability, it is very important that we first lay the groundwork with some vocabulary.

An experiment is any activity involving chance, which could be anything like pulling a random card, flipping a coin, rolling dice, or even spinning a spinner in a game like Twister.

A single trial is performing or observing the experiment. For example, each time we pull a card from the deck, that is one trial.

Each possible result is the outcome of the trial. So, if I flip a coin once and it lands heads-up, that is my outcome.

The collection of all outcomes is called the sample space. Flipping a coin means that the coin will land either heads or tails up, so the sample space is heads or tails. This can be written as {H,T} for heads or tails.

Try to guess the sample space (S) of flipping a coin twice.

• What are my possible outcomes from flipping a coin twice?

{HH, HT, TH, TT} Heads then Heads, Heads then Tails, etc.

• What is the sample space for the spinner below?

{red, blue, green, yellow}

An event or success is an outcome or set of outcomes from an experiment.

For example, our event for the spinner could be landing on yellow, or not landing on green (our sample space for "not" statements is everything else, in this case {yellow, blue, red}).

Probability, therefore, is the measurement of how likely something is to occur. Probability is normally written as fractions, decimals, ratios, or as a percent.

Whenever we add all the probabilities of an experiment together, it must equal 1 or 100%.

Take a look at the graph below.

• What do you notice about the probability of the event actually happening as related to the chance that it is likely to occur?
• Did you notice that the greater the chance, the greater the probability?

Consider the following examples:

• What is the probability that there are 31 days in August?

Certain, since there are always 31 days in August.

• What about the probability of a coin landing heads-up?

Even chance because heads is one of only two outcomes.

Experimental probability is the ratio of the number of times the event happened to the number of trials. We can then use that probability to guess, or predict, what the next result will be.

The more trials we conduct, the more accurate our prediction will be of the actual probability. Ask John Kerrich the best way to flip a coin!

Another, more practical way to write the most important rule when it comes to experimental probability is this:

So, if we go back to our coin example, and we flip the coin 10 times and it lands on heads 4 times, then our experimental probability for that would be ⁴⁄₁₀ or, as a simplified fraction, ²⁄₅.

• What would be our experimental probability for landing on red if we spun 20 times and landed on red 7 times?

Remember, wherever possible, you should reduce or simplify your fractions.

Now that we have a foundation of how to work with probability, and have covered all the major terms, let's try some practice in the Got It? section.