Respuesta :
Answer:
[tex]\frac{2}{3}[/tex].
Step-by-step explanation:
We are told that a spinner has equal regions numbered 1 through 21.
We can see that our both events are not mutually exclusive events, so will use formula [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex] to find our desired probability.
[tex]P(A\cup B)[/tex] = Probability of event A or event B.
[tex]P(A)[/tex] = Probability of event A.
[tex]P(B)[/tex] = Probability of event B.
[tex]P(A\cap B)[/tex] = Probability of event A and event B.
Let us find probability that spinner will stop on an even number. Even numbers on spinner's region are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
[tex]P(\text{ Spinner will stop on an even number})=\frac{10}{21}[/tex]
Now let us find probability that spinner will stop on a multiple of 3. Multiples of 3 on the spinner's region are: 3,6,9,12,15,18,21.
[tex]P(\text{ Spinner will stop on a multiple of 3})=\frac{7}{21}[/tex]
Now we have to figure out probability that spinner will stop on an even number and multiple of 3. Both events happening at one time are: 6,12,18.
[tex]P(\text{Spinner will stop on an even number and multiple of 3})=\frac{3}{21}[/tex]
Now let us substitute our values in above mentioned formula.
[tex]P(\text{Spinner will stop on an even number or multiple of 3})=\frac{10}{21}+\frac{7}{21}-\frac{3}{21}[/tex]
[tex]P(\text{Spinner will stop on an even number or multiple of 3})=\frac{17}{21}-\frac{3}{21}[/tex]
[tex]P(\text{Spinner will stop on an even number or multiple of 3})=\frac{14}{21}=\frac{2}{3}[/tex]
Therefore, probability that the spinner will stop on an even number or a multiple of 3 is [tex]\frac{2}{3}[/tex].
Using it's concept, it is found that there is a 0.6667 = 66.67% probability that the spinner will stop on an even number or a multiple of 3.
What is a probability?
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 21 possible outcomes for the spinner.
- 10 of those are even numbers.
- 4 of those are odd numbers which are multiples of 3.
Hence:
[tex]p = \frac{14}{21} = \frac{2}{3} = 0.6667[/tex]
0.6667 = 66.67% probability that the spinner will stop on an even number or a multiple of 3.
More can be learned about the probability concept at https://brainly.com/question/15536019
