Sure, let's go through each scenario one by one and determine the theoretical probability of each event happening.
1. Spinning a number less than 3:
- Numbers less than 3 on the spinner are 1 and 2.
- This gives us 2 favorable outcomes.
- Total possible outcomes: 10
- Probability = [tex]\( \frac{2}{10} \)[/tex] = 0.2 or [tex]\( \frac{1}{5} \)[/tex].
2. Spinning a 4 or 5:
- Numbers in this event are 4 and 5.
- This gives us 2 favorable outcomes.
- Total possible outcomes: 10
- Probability = [tex]\( \frac{2}{10} \)[/tex] = 0.2 or [tex]\( \frac{1}{5} \)[/tex].
3. Spinning an odd number:
- Odd numbers on the spinner are 1, 3, 5, 7, and 9.
- This gives us 5 favorable outcomes.
- Total possible outcomes: 10
- Probability = [tex]\( \frac{5}{10} \)[/tex] = 0.5.
4. Spinning a number greater than 8:
- Numbers greater than 8 on the spinner are 9 and 10.
- This gives us 2 favorable outcomes.
- Total possible outcomes: 10
- Probability = [tex]\( \frac{2}{10} \)[/tex] = 0.2 or [tex]\( \frac{1}{5} \)[/tex].
5. Spinning a number less than 8:
- Numbers less than 8 on the spinner are 1, 2, 3, 4, 5, 6, and 7.
- This gives us 7 favorable outcomes.
- Total possible outcomes: 10
- Probability = [tex]\( \frac{7}{10} \)[/tex] = 0.7.
From the calculations, the events that have a theoretical probability of exactly [tex]\( \frac{1}{5} \)[/tex] are:
- Spinning a number less than 3
- Spinning a 4 or 5
- Spinning a number greater than 8
So, the three selected options with a probability of [tex]\( \frac{1}{5} \)[/tex] are:
- Spinning a number less than 3
- Spinning a 4 or 5
- Spinning a number greater than 8
