Let's break down each part of the problem step by step.
### Part (a)
How many times did they spin the spinner in total?
To find the total number of spins, we need to sum the frequencies of the spinner landing on each of the colors.
- The frequency for Orange = 5
- The frequency for Green = 4
- The frequency for Black = 9
So, the total number of spins is:
[tex]\[ 5 \text{ (Orange)} + 4 \text{ (Green)} + 9 \text{ (Black)} = 18 \][/tex]
Thus, the total number of spins is 18.
### Part (b)
Work out the relative frequency of the spinner landing on green. Give your answer as a fraction in its simplest form.
First, relative frequency is calculated as:
[tex]\[ \text{Relative Frequency of Green} = \frac{\text{Frequency of Green}}{\text{Total Number of Spins}} \][/tex]
From the table:
- Frequency of Green = 4
- Total Number of Spins = 18
So, the relative frequency of landing on Green is:
[tex]\[ \frac{4}{18} \][/tex]
Next, we need to simplify this fraction. To do this, we find the greatest common divisor (GCD) of 4 and 18, and then divide both the numerator and the denominator by this GCD.
In this case, the GCD of 4 and 18 is 2.
Now, divide both the numerator and the denominator by 2:
[tex]\[ \frac{4 \div 2}{18 \div 2} = \frac{2}{9} \][/tex]
Therefore, the relative frequency of the spinner landing on green, simplified, is:
[tex]\[ \frac{2}{9} \][/tex]
### Conclusion
a) Samuel spun the spinner a total of 18 times.
b) The relative frequency of the spinner landing on green, in its simplest form, is [tex]\(\frac{2}{9}\)[/tex].
