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?
Okay so I am lost. I understand that the probability of an event is
the # of ways an event can occur over the total # of possible outcomes.
I need some explaining done. Please
List the numbers from 1 to 21 which are either even or multiples of 3:
2,3,4,6,8,9,10,12,14,15,16,18,20,12
I count 14, not 17.
Prob(event as stated) = 14/21 = 2/3
Ok. I counted some numbers twice. I needed to write the numbers out like you did. Thanks
Of course! Let's break this down step by step.
First, let's determine the total number of possible outcomes. In this case, we are given that the spinner has regions numbered 1 through 21. Therefore, the total number of possible outcomes is 21.
Next, let's identify the number of favorable outcomes. We want the spinner to stop on either an even number or a multiple of 3.
To find the number of even numbers from 1 to 21, we need to consider that an even number is divisible by 2. Therefore, we have 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) in the range from 1 to 21.
To find the number of multiples of 3 from 1 to 21, we need to consider numbers that can be divided by 3 without any remainder. The multiples of 3 in this range are 3, 6, 9, 12, 15, 18, 21, which gives us a total of 7 multiples of 3.
Now, we need to ensure that we don't count any number twice. There are two numbers, 6, 12, that appear in both the list of even numbers and multiples of 3. Therefore, we need to subtract one of these duplicated numbers.
Summing up the counts, we have a total of 10 + 7 - 1 = 16 favorable outcomes.
Finally, we can use the probability formula to find the probability of the spinner stopping on an even number or a multiple of 3:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 16 / 21
Thus, the probability that the spinner will stop on an even number or a multiple of 3 is 16/21.
Would the total possible outcomes be 17?
The number of evens would be 10 and the multiply of 3 is 7. So 10 and 7 together is 10.