Alright, let's break down the problem step by step.
a) Which number is the spinner most likely to land on?
A fair spinner with 8 equal sections means each section has an equal probability of being landed on. Since the spinner is fair and all sections are equal, no single number is more likely to be landed on than any other. Hence, each number is equally likely to be spun.
Thus, there is no single number that is more likely to be landed on. The probability for each number is the same.
b) Select the term from the list below that best describes the probability of the spinner landing on a 1.
We know from part (a) that any specific number has an equal chance of being landed on. Since there are 8 equal sections, the probability of the spinner landing on any particular number, such as 1, is given by the formula for probability:
[tex]\[ P(\text{landing on 1}) = \frac{1}{8} \][/tex]
This probability is 0.125 (or 12.5%).
Looking at the provided terms:
- Impossible (0% or 0)
- Unlikely (between 0% and 50%)
- Even chance (50%)
- Likely (greater than 50%)
- Certain (100% or 1)
The probability of 0.125 or 12.5% fits the description of "Unlikely."
Therefore, the term that best describes the probability of the spinner landing on a 1 is "Unlikely."
c) Draw a [tex]$\times$[/tex] on the scale below to mark the probability of the spinner landing on a 3.
We already established that each number from 1 to 8 has the same likelihood of being landed on. Therefore, the probability of landing on a 3 is also [tex]\(\frac{1}{8}\)[/tex] or 0.125.
On a typical probability scale ranging from 0 to 1:
- 0 (Impossible)
- 0.5 (Even chance)
- 1 (Certain)
A mark at 0.125 would be closer to 0 than to 0.5. Here's how you might visually represent it:
```plaintext
0 0.25 0.50 0.75 1.00
|-----|------|------|------|
\
0.125
```
The `[tex]$\times$[/tex]` should be placed at the 0.125 mark, which is closer to 0 than to 0.25.
So to summarize:
a) No single number is more likely to be landed on; each number has an equal probability.
b) The best term to describe the probability of landing on a 1 is "Unlikely."
c) The mark at [tex]\(\times\)[/tex] on the probability scale is at 0.125.
