Question

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Theoretical Probabilities of Repeated Events Practice
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Question
Use the image to answer the question.

An illustration of a circle with four equal differently colored parts labeled 1, 2, 3, 4 clockwise. An arrow starting at the center points toward 1.

The spinner is spun twice. What is the probability of spinning an even number on both spins? Express your answer as a simplified fraction.

(1 point)

Answer 1

To find the probability of spinning an even number on both spins of the spinner, we first need to identify the even numbers in the colored sections:

In this case, the sections are labeled 1, 2, 3, and 4. The even numbers among these are:
- 2
- 4

This gives us a total of 2 even numbers.

The total number of sections on the spinner is 4.

So, the probability of spinning an even number on a single spin is:

\[
P(\text{even}) = \frac{\text{number of even numbers}}{\text{total sections}} = \frac{2}{4} = \frac{1}{2}
\]

Since the spinner is spun twice, we want to find the probability of spinning an even number on both spins. The events are independent, so we can multiply the probabilities for each spin:

\[
P(\text{even on first spin and even on second spin}) = P(\text{even}) \times P(\text{even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

Thus, the probability of spinning an even number on both spins is:

\[
\boxed{\frac{1}{4}}
\]