a To determine the probability of spinning a certain region, we have to consider the central angle of each letter.
B
b There are two vowels, A and E.
A
a 1/8
B
b 5/6
Practice makes perfect
a The probability of obtaining the different regions in each of the spinners is the central angle divided by 360^(∘).
With this information we can draw a tree diagram and highlight the path of spinning A, C, and E.
To calculate the probability of the given event happening, we have to multiply the probabilities along the highlighted path.
P(A,C,E)=(3/4)(1/2)(1/3)=3/24
The probability of spinning A, C, and E is 324, which we can reduce to 18.
b Of the 7 letters there are 2 vowels: A and E. Since getting A on the first spinner will result in at least one vowel no matter the outcome of the second and third spinner, we will instead calculate the result of not spinning a vowel and then determine the complement of this event.
We have four paths through the tree diagram that result in no vowel being spun. Similar to Part A, we have to multiply the probabilities along each path to determine the probability of that event. By adding the probabilities we can determine the probability of not spinning a vowel.
P(No vowel): (1/4)(1/2)(1/3)4=4/24
Finally, we calculate the complement of P(No vowel).
