There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 3?
1/15
To find the probability, we need to determine the number of favorable outcomes (results that are multiples of 5 or multiples of 3) and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
Multiples of 5: 5, 10, 15 (3 outcomes)
Multiples of 3: 3, 6, 9, 12, 15 (5 outcomes, but we already included 15 in multiples of 5, so we only count it once)
Total favorable outcomes: 3 + 4 = 7
Step 2: Determine the total number of possible outcomes:
There are 15 equally likely outcomes on the spinner, numbered 1 through 15.
Step 3: Calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 7 / 15
Probability ≈ 0.4667 or 46.67% (rounded to the nearest hundredth)
To find the probability that the result is a multiple of 5 or a multiple of 3, we need to calculate the number of favorable outcomes (outcomes that are multiples of 5 or multiples of 3) and divide it by the total number of possible outcomes.
First, let's determine the number of multiples of 5 between 1 and 15. The multiples of 5 are 5 and 10.
Next, let's determine the number of multiples of 3 between 1 and 15. The multiples of 3 are 3, 6, 9, and 12.
Notice that the number 15 is a multiple of both 5 and 3 (it is their common multiple). However, we should only count it once, so we subtract it from the total.
So, the favorable outcomes are 5, 10, 3, 6, 9, and 12, for a total of 6 outcomes.
Now, let's calculate the total number of possible outcomes. Since the spinner has 15 equal areas, the total number of possible outcomes is 15.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total possible outcomes
Probability = 6/15 = 2/5
So, the probability that the result is a multiple of 5 or a multiple of 3 when the spinner is spun one time is 2/5.
multiples of 3: 3, 6, 9, 12, 15
multiples of 5: 5, 10, 15
total of your event = 7 , can't count 15 twice
prov(your event) = 7/15