Question

A student is playing a game with two spinners:


Spinner A has 4 equal sections: red, blue, green, yellow.


Spinner B has 8 equal sections: red, blue, green, yellow, orange, purple, white, black.


The student wins if they spin red.

Which statement best compares the probabilities of winning on Spinner A vs. Spinner B?
(4 Points)

The probability of spinning red is the same for both spinners.

It is more likely to spin red on Spinner A than on Spinner B.

It is more likely to spin red on Spinner B than on Spinner A.

It is impossible to spin red on either spinner.

Answer 1

To determine the probabilities of winning on Spinner A and Spinner B, let's calculate the probability of spinning red on each spinner.

**Spinner A:**
- Spinner A has 4 equal sections: red, blue, green, yellow.
- The probability of spinning red is:
\[
P(\text{red on A}) = \frac{\text{Number of red sections}}{\text{Total sections}} = \frac{1}{4}
\]

**Spinner B:**
- Spinner B has 8 equal sections: red, blue, green, yellow, orange, purple, white, black.
- The probability of spinning red is:
\[
P(\text{red on B}) = \frac{\text{Number of red sections}}{\text{Total sections}} = \frac{1}{8}
\]

Now we can compare the probabilities:

- Probability of red on Spinner A: \(\frac{1}{4} = 0.25\)
- Probability of red on Spinner B: \(\frac{1}{8} = 0.125\)

Since \(0.25 > 0.125\), it is more likely to spin red on Spinner A than on Spinner B.

Therefore, the best statement to compare the probabilities of winning on Spinner A vs. Spinner B is:

**"It is more likely to spin red on Spinner A than on Spinner B."**