a The probability of getting a certain field is the angle it occupies of the spinner divided by 360^(∘).
B
b Note that getting a sum of 8 can be obtained in two different ways.
A
a 1/12
B
b 1/3
Practice makes perfect
a The only way to achieve a sum of 4 is if you get a 2 on both spinners. To identify this probability we have to determine how large an area these sectors occupy of their respective circles.
Spinner #1
From the diagram, we see that the sector with a 2 has a right angle. Therefore, it occupies 90^(∘)360^(∘)= 14 of the circle and the second sector occupies the remaining part, 34.
Spinner #2
In the second spinner each field occupies a third of the circle. Therefore, the probability of getting a 2 on the second spinner is 120^(∘)360^(∘)= 13. We get the following diagram.
Tree Diagram
We can illustrate getting two 2's with a tree diagram.
To calculate the probability of getting 2 twice — in other words a sum of 4 — we have to multiply the individual probabilities of these events.
P(sum is 4)=1/4* 1/3=1/12
b To obtain a sum of 8, we have two paths to consider. Either we can get a 4 on both spinners, or, we can get a 2 on the first spinner and a 6 on the second spinner. Let's mark these paths in our tree diagram from Part A.
Like in Part A, we can calculate P(2,6) and P(4,4) by multiplying the individual probabilities.
P(2,6)=1/4* 1/3=1/12 [0.8em]
P(4,4)=3/4* 1/3=3/12
By adding these individual probabilities we get the total probability of getting a sum of 8.
