Find probabilities from spinners

For a spinner divided into equally sized sections, probability is determined by the ratio of favorable sections to total sections, expressed as a fraction and, when appropriate, as a decimal or percent. The understanding includes identifying the sample space, combining sections with the same favorable outcome, comparing events, and recognizing that probabilities of complementary outcomes sum to 1; unequal-area spinners and more advanced conditional probability are outside this scope.

Detailed Explanation: Find probabilities from spinners

A spinner’s probability depends on how many equal-sized sections match the event you are looking for.

Use:

\text{Probability}=\frac{\text{number of favorable sections}}{\text{total number of sections}}

Example

A spinner has $8$ equal sections:

$3$ red sections
$2$ blue sections
$2$ green sections
$1$ yellow section

What is the probability of landing on blue or green?

Step 1: Count the total sections.

There are $8$ sections altogether, so the sample space has $8$ possible outcomes.

Step 2: Count the favorable sections.

A favorable outcome is landing on blue or green:

2+2=4

There are $4$ favorable sections.

Step 3: Write the probability as a fraction.

P(\text{blue or green})=\frac{4}{8}

Step 4: Simplify the fraction and convert if needed.

\frac{4}{8}=\frac{1}{2}=0.5=50\%

So, the probability of landing on blue or green is:

\boxed{\frac{1}{2},\ 0.5,\text{ or }50\%}

Remember to combine all sections that match the event. The probability of landing on a color and the probability of not landing on that color add up to $1$ , or $100\%$ .

Learn by doing: Find probabilities from spinners

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Probability - Spinner, One Spin, Multiple Answers, To Fraction

Earned ?