Determine whether the events are mutually exclusive.
-A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3?
A) $\frac { 2 } { 3 }$
B) 12
C) $\frac { 1 } { 3 }$
D) $\frac { 7 } { 9 }$

Question

Determine whether the events are mutually exclusive.
-A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3? 
A) $\frac { 2 } { 3 }$
B) 12
C) $\frac { 1 } { 3 }$
D) $\frac { 7 } { 9 }$

Quizplus · Accepted Answer

The events are not mutually exclusive because numbers that are both even and multiples of 3 (such as 6 and 12) are included in both categories. To find the probability, list the even numbers (2, 4, 6, 8, 10, 12, 14) and the multiples of 3 (3, 6, 9, 12, 15). Combining these without repetition gives 10 unique numbers (2, 3, 4, 6, 8, 9, 10, 12, 14, 15) out of 15, so the probability is $\frac{10}{15} = \frac{2}{3}$.

Determine Whether the Events Are Mutually Exclusive 23\frac { 2 } { 3 }32​

Determine Whether the Events Are Mutually Exclusive $\frac { 2 } { 3 }$