A student is playing a game with two spinners:

Question

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 spinning red on Spinner A and Spinner B, we need to calculate the probability for each spinner.

Spinner A:

• It has 4 equal sections: red, blue, green, yellow.
• The probability of spinning red is the number of favorable outcomes (1) divided by the total number of outcomes (4).

\[ P(\text{red on Spinner A}) = \frac{1}{4} \]

Spinner B:

• It has 8 equal sections: red, blue, green, yellow, orange, purple, white, black.
• The probability of spinning red is also the number of favorable outcomes (1) divided by the total number of outcomes (8).

\[ P(\text{red on Spinner B}) = \frac{1}{8} \]

Now, let's compare the probabilities:

• \( \frac{1}{4} \) is greater than \( \frac{1}{8} \).

Therefore, it is more likely to spin red on Spinner A than on Spinner B.

The correct statement is: It is more likely to spin red on Spinner A than on Spinner B.