Probably Yes, Probably No: Probability

Lesson Plan - Get It!

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Probability is the measure of how likely it is for an event to happen.

Some situations have uncertain futures, such as the weather or the arrival of a train or airplane. The forecast might say it will rain tomorrow, but that is only an educated guess. It might or might not rain. Since we do not know for sure, we say there is a "chance of rain" or say it is "very likely" that it will rain.

The probability of an event occurring can be described as certain, likely, unlikely, or impossible. If an event cannot happen, its probability is 0. If an event is certain to happen, its probability is 1. Probability can be expressed as a fraction with the number of favorable outcomes as the numerator and the number of possible outcomes as the denominator. As you may recall, numerator is the top of a fraction and denominator is the bottom number of a fraction.

Example 1

A standard dot cube has six faces. Each face has dots representing the numbers 1-6. Pretend you roll the cube once. Which word best describes each event: certain (100%), likely (more than 50%), unlikely (less than 50%) , or impossible (0%)?

1. The cube will stop with 4 dots on top.
   • Unlikely — there are six faces but only one has 4 dots.
2. The cube will stop with more than 2 dots on top.
   • Likely, because of the six faces on the dot cube — four have more than 2 dots. It would be expected that a number greater than 2 would end up on top more than half the times the cube is rolled.
3. The cube will stop with fewer than 8 dots on top.
   • Certain, because all of the faces have fewer than 8 dots. Every time the cube is rolled, the face on top will have fewer than 8 dots.
4. The cube will stop with more than 6 dots on top.
   • Impossible — none of the faces have more than 6 dots, so this could never happen.

Example 2

A bag contains 6 red marbles, 4 blue marbles, and 2 yellow marbles. Suppose you pick one marble from the bag without looking.

• Find the probability that the marble is red.
• Find the probability that the marble is not red.

There are 12 marbles total and 6 are red. So, 6 out of 12 marbles are red. This could also be viewed as a 50%. The probability that the marble is not red is also 6 out of 12 because if 6 are red, that means 6 are not red. This could also be viewed as a 50%.

Example 3

Use the circle below to answer the following problems:

1. What is the probability that the spinner will stop on 4? Since there are four total parts and only one section that is labeled 4, the probability would be unlikely, or 1 out of 4.
2. What is the probability of spinning a number greater than 2? Since there two parts with a value greater than 2, the probability would be 2 out of 4. This could also be viewed as a 50%.
3. What is the probability of spinning an even number? Since there are four parts and two of the values are even, the probability would be ²⁄₄ or 50%.
4. What is the probability that the spinner will stop on a number greater than 5? Since there are no values greater than 5, there would be a 0% probability, or an impossible chance.

Many experiments involve probability, such as tossing a coin, spinning a spinner, and selecting an object from a collection of objects.

• Discuss with an adult or teacher an experiment or event that has a "likely" outcome.
• Then, discuss an experiment or event that would have an "impossible" outcome.

In the Got It? section, you will practice finding the outcomes of different probability situations using online games and interactive activities.