A circular spinner has 12 equal sections. Which of the following are possible probabilities for any event involving a single spin of this spinner? Select all that apply.
To determine the possible probabilities for any event involving a single spin of the circular spinner, we need to consider the number of sections involved in the event.
1. If the event involves a single section, there are 12 possible outcomes (equal sections) and the probability can be calculated as 1/12.
2. If the event involves two adjacent or neighboring sections (for example, two consecutive sections), there are also 12 adjacent pairs, so the probability can be calculated as 2/12 or simplified as 1/6.
3. If the event involves two non-adjacent sections (for example, skip one section), there are 6 possible pairs. The probability can be calculated as 2/12 or simplified as 1/6.
4. If the event involves three adjacent sections (for example, three consecutive sections), there are 12 possible triplets. The probability can be calculated as 3/12 or simplified as 1/4.
5. If the event involves four adjacent sections (for example, four consecutive sections), there are 12 possible quadruplets. The probability can be calculated as 4/12 or simplified as 1/3.
6. If the event involves six adjacent sections (for example, half of the spinner), there is only one possible outcome. The probability is 1/12.
Therefore, the possible probabilities for any event involving a single spin of the spinner are:
- 1/12
- 1/6
- 1/6
- 1/4
- 1/3
- 1/12
To find the possible probabilities for any event involving a single spin of this spinner, we need to understand the concept of probability.
Probability is a measure of how likely an event is to occur. It is typically expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
In this case, the spinner has 12 equal sections. Since each section is equal, the probability of the spinner landing on any specific section is the same for each section. To find the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.
Now, let's analyze the given options one by one:
Option 1: 0.5
Since the spinner has 12 equal sections, the probability of landing on any individual section is 1/12. Therefore, 0.5 (or 1/2) is not a possible probability.
Option 2: 0.25
Again, the probability of landing on any individual section is 1/12. Therefore, 0.25 (or 1/4) is not a possible probability.
Option 3: 0.083
To determine if this probability is possible, we need to express it as a fraction. If we simplify 0.083, it becomes 83/1000. Since 83/1000 is not a fraction with a denominator of 12, 0.083 is not a possible probability.
Option 4: 0.091
Similar to the previous step, we can express 0.091 as a fraction. In this case, 0.091 simplifies to 91/1000. Again, 91/1000 does not have a denominator of 12, so 0.091 is not a possible probability.
Option 5: 0.0833
Converting 0.0833 to a fraction yields 833/10,000. It is evident that 833/10,000 is not a fraction with a denominator of 12, so 0.0833 is not a possible probability.
Option 6: 1/12
As previously mentioned, the probability of landing on any individual section is 1/12. Therefore, 1/12 is a possible probability.
In conclusion, the only possible probability for any event involving a single spin of this spinner is 1/12.