Find the indicated probability by using the general addition rule.
-A spinner has regions numbered 1 through 21 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?
A)$\frac { 10 } { 9 }$
B) 17
C) $\frac { 1 } { 3 }$
D) $\frac { 2 } { 3 }$

Question

Find the indicated probability by using the general addition rule.
-A spinner has regions numbered 1 through 21 . What is the probability that the spinner will stop on an even number or a multiple of 3 ?  
A)$\frac { 10 } { 9 }$
B) 17
C) $\frac { 1 } { 3 }$
D) $\frac { 2 } { 3 }$

Quizplus · Accepted Answer

The even numbers between 1 and 21 are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, making 10 even numbers. The multiples of 3 between 1 and 21 are 3, 6, 9, 12, 15, 18, and 21, making 7 multiples of 3. However, 6, 12, and 18 are both even and multiples of 3, so they are counted twice if we simply add the two sets. To avoid double-counting, we subtract the numbers that are both even and multiples of 3, which are 3 numbers. So, we have 10 (even numbers) + 7 (multiples of 3) - 3 (duplicates) = 14 unique numbers that are either even or multiples of 3 out of 21. Therefore, the probability is $ \frac{14}{21} = \frac{2}{3} $.

Find the Indicated Probability by Using the General Addition Rule 109\frac { 10 } { 9 }910​

Find the Indicated Probability by Using the General Addition Rule $\frac { 10 } { 9 }$