Choose a natural number between 1 and 30, inclusive. What is the probability that the number is a multiple of 3?
multiples of 3 are
3 6 9 12 15 18 21 24 27 and 30
that is, there are 10 of them
so prob = 10/30 = 1/3
(makes sense, just like the prob that picking a number from 1 to 40, which is a multiple of 4 would be 1/4)
To find the probability that a number between 1 and 30, inclusive, is a multiple of 3, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
In this case, the total number of possible outcomes is 30 since we are choosing a number between 1 and 30.
Now, let's determine the number of favorable outcomes, which are the multiples of 3 between 1 and 30. The multiples of 3 in this range are: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. There are a total of 10 multiples of 3 within this range.
Therefore, the probability of choosing a number between 1 and 30 that is a multiple of 3 is:
Number of favorable outcomes / Total number of possible outcomes
= 10 / 30
= 1/3
So, the probability that the number chosen is a multiple of 3 is 1/3.