GED Mathematical Reasoning: Probability I

  • A probability can be written as a fraction, decimal, or percent. Also, a probability can have a value from zero or 0% (which means the event will NOT happen) to one or 100% (which means the event is certain to happen). So if you solve a probability exercise and get an answer that’s outside of this range, you know something is wrong and can go back to check your work for a mistake.
  • As a real life instance of probability, you have probably heard a weather forecaster say something like: “there is a 20% chance of rain today”. This example illustrates another important point related to probability. That is: Probability is not an exact science – it is only used to tell the likelihood of something, it does not tell for sure what will happen.
  • In the study of probability, each possible result is called an OUTCOME. When we are trying to find the probability of a specific outcome, we call that our FAVORABLE OUTCOME. These outcomes are called the “favorable” outcomes, since rolling an even number is what we’re interested in. So there are THREE ways of achieving a favorable outcome in this situation.
  • The probability of a favorable outcome can be expressed as a fraction where the number of ways to achieve the favorable outcome is in the numerator and the total number of possible outcomes is in the denominator.

prob. of favorable outcome = \frac{number\, of\, favorable\, outcomes}{total\, number\, of\, possible\, outcomes}

  • When writing a probability as a fraction it is standard practice to reduce to lowest terms if possible.

 

Example 1

In a vending machine game, there are plastic bubbles containing prizes. Two of the bubbles contain a cash prize, six bubbles contain a toy prize, and ten bubbles contain a candy prize. If Sandy plays the vending machine game and randomly chooses a bubble, what is the probability that she will pick one containing a cash prize? Express the answer as a fraction in lowest terms.

 

Relating this to our example, when Sandy picks a bubble there are a total of 18 possible outcomes, because there are 18 bubbles in the machine. Since we are interested in the probability of Sandy choosing a bubble containing a cash prize, then that represents the favorable outcome. And since two bubbles contain a cash price, that means there are two favorable outcomes.

The probability of a favorable outcome can be expressed as a fraction where the number of favorable outcomes is in the numerator and the total number of possible outcomes is in the denominator.

Prob. of a favorable outcome = \frac{number\, of\, favorable\, outcomes}{total\, number\, of\, possible\, outcomes}

So the probability of Sandy selecting a bubble containing a cash prize can be written as a fraction where the number in the numerator will be 2 and the number in the denominator will be 18.

prob. of a cash prize = \frac{2}{18} = \frac{1}{9}

Now, suppose we would like to express this probability as a percent.

To turn the fraction \frac{1}{9} into a percent, we first need to turn it into a decimal. One divided by nine yields: .111…  To turn this decimal into a percent, we’ll simply move the decimal point to the right, two places and add a “percent” sign for a result of:  11.1%

In conclusion, understanding probability can be useful for making predictions. We may not be able to say for sure which prize bubble Sandy will choose, but we can determine how likely a certain outcome might be. Based on the answer of 11.1%, it is not very likely that Sandy will pick a bubble containing a cash prize.

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