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Describe probability using fractions, decimals, and percents

Probability measures how likely an event is, from 0 for an impossible event to 1 for a certain event, or equivalently from 0% to 100%; for equally likely outcomes, it can be represented as the fraction of favorable outcomes out of all possible outcomes. The same probability may be expressed as an equivalent fraction, decimal, or percent, supporting comparison and interpretation on a probability scale and reinforcing proportional reasoning. Conditional probability and more advanced probability models are not included.

Detailed Explanation: Describe probability using fractions, decimals, and percents

Probability tells how likely an event is to happen.

  • 00 or 0%0\% means impossible.
  • 11 or 100%100\% means certain.
  • Values between 00 and 11 show different levels of likelihood.

For equally likely outcomes,

Probability=number of favorable outcomestotal number of outcomes.\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}.

Example

A spinner has 88 equal sections. 33 sections are blue. What is the probability of landing on blue as a fraction, decimal, and percent?

Step 1: Write the probability as a fraction.

There are 33 favorable outcomes and 88 total outcomes:

P(blue)=38.P(\text{blue})=\frac{3}{8}.

Step 2: Convert the fraction to a decimal.

Divide the numerator by the denominator:

3÷8=0.375.3\div 8=0.375.

So, the probability as a decimal is 0.3750.375.

Step 3: Convert the decimal to a percent.

Multiply the decimal by 100100 and add the percent sign:

0.375×100=37.5.0.375\times 100=37.5.

So, the probability as a percent is 37.5%37.5\%.

Therefore, the probability of landing on blue is

38=0.375=37.5%.\boxed{\frac{3}{8}=0.375=37.5\%}.

This means landing on blue is possible, but it is less likely than not landing on blue because 37.5%37.5\% is less than 50%50\%.

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