Geometry

Question Analysis
This question involves calculating the probability of events that are not strictly mutually exclusive at first glance, but can be analyzed using the principle of mutually exclusive sub - events.
The main focus is on identifying the prime numbers () and multiples of 4 () on the spinner, and then using the addition rule for mutually exclusive events by considering non - overlapping parts of these sets.

Key Concept Explanation
When dealing with events that may have an overlap, we can break them down into mutually exclusive sub - events.
Mutually exclusive events have no common outcomes, and for such events, the probability of their union is the sum of their individual probabilities. P(A ∪ B) = P(A) + P(B)

Step - by - Step Solution
Identify the favorable outcomes for each event:
Prime numbers on the spinner: , so there are 4 prime numbers.
Multiples of 4 on the spinner: , so there are 2 multiples of 4.
Notice that there is no overlap between the set of prime numbers and the set of multiples of 4 in this case.
Calculate the probabilities of these mutually exclusive sub - events:
The probability of spinning a prime number, .
The probability of spinning a multiple of 4,

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