Question
. An experiment consists of spinning the spinner below and flipping a coin.
What is the probability of the spinner landing on 9 or 11 and getting tails on the coin?
Responses
1/8
1/12
1/4
1/6
What is the probability of the spinner landing on 9 or 11 and getting tails on the coin?
Responses
1/8
1/12
1/4
1/6
Answers
GPT-4o mini
To find the probability of the spinner landing on 9 or 11 and getting tails on the coin, we first need to determine the probability of each individual event and then combine the probabilities.
Assuming the spinner has an equal number of outcomes, let's outline the steps to find the overall probability:
1. **Count favorable outcomes on the spinner**: We need to find the total number of sections on the spinner that include 9 and 11. Let's assume the spinner has numbers ranging from 1 to n. If we assume the spinner has numbers 1 to 12 (which is common), then the favorable outcomes for landing on either 9 or 11 are 2 (the numbers 9 and 11).
2. **Calculate the total outcomes on the spinner**: If we assume the spinner sections are numbered 1 to 12, then there are a total of 12 sections.
3. **Probability of landing on 9 or 11**:
\[
P(\text{9 or 11}) = \frac{2 \text{ favorable outcomes}}{12 \text{ total outcomes}} = \frac{2}{12} = \frac{1}{6}
\]
4. **Probability of flipping tails on the coin**: The coin has 2 outcomes (heads and tails), and with 1 favorable outcome of getting tails:
\[
P(\text{tails}) = \frac{1}{2}
\]
5. **Combine the probabilities**: The events (spinner and coin flip) are independent, so we multiply the probabilities together:
\[
P(\text{9 or 11 and tails}) = P(\text{9 or 11}) \times P(\text{tails}) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}
\]
Therefore, the probability of the spinner landing on 9 or 11 and getting tails on the coin is \( \frac{1}{12} \).
**Final answer: 1/12**.
Assuming the spinner has an equal number of outcomes, let's outline the steps to find the overall probability:
1. **Count favorable outcomes on the spinner**: We need to find the total number of sections on the spinner that include 9 and 11. Let's assume the spinner has numbers ranging from 1 to n. If we assume the spinner has numbers 1 to 12 (which is common), then the favorable outcomes for landing on either 9 or 11 are 2 (the numbers 9 and 11).
2. **Calculate the total outcomes on the spinner**: If we assume the spinner sections are numbered 1 to 12, then there are a total of 12 sections.
3. **Probability of landing on 9 or 11**:
\[
P(\text{9 or 11}) = \frac{2 \text{ favorable outcomes}}{12 \text{ total outcomes}} = \frac{2}{12} = \frac{1}{6}
\]
4. **Probability of flipping tails on the coin**: The coin has 2 outcomes (heads and tails), and with 1 favorable outcome of getting tails:
\[
P(\text{tails}) = \frac{1}{2}
\]
5. **Combine the probabilities**: The events (spinner and coin flip) are independent, so we multiply the probabilities together:
\[
P(\text{9 or 11 and tails}) = P(\text{9 or 11}) \times P(\text{tails}) = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}
\]
Therefore, the probability of the spinner landing on 9 or 11 and getting tails on the coin is \( \frac{1}{12} \).
**Final answer: 1/12**.