Question

Suppose an integer is selected at random from the set of integers S={1,2,3,...29,30}.
(1) Find the probability that it is divisible by at least one of the numbers 2,3,or 5
(2) Find the probability that it is divisible by exactly one of the numbers 2,3,or 5.

Answer 1

Define your sample space.

Answer 2

S={1,2,......29,30}

Answer 3

There are 15 numbers divisible by 2, 10 numbers divisible by 3, and 6 numbers divisible by 5.

Answer 4

The sample space are the possible outcomes, i.e. it's either divisible by 2 or it's not; it's either divisible by 3 or it's not, etc.

Answer 5

ok

Answer 6

hmmm
i would say the sample space would be all possible outcomes, defined above by @oswalde2000

Answer 7

I thought that was the population space.

Answer 8

Wouldn't separate sets need to be defined to compute the probabilities?

Answer 9

maybe it is semantics. usually one defines the sample space as the set of all possible outcomes.
then an "event" would be something like "the number is divisible by 2" or "the number is divisible by 2, 3 or 5"

Answer 10

that way, using the uniform (equally likely) distribution, you would calculate the probability by the number of elements in the event divided by the number of elements in the sample space

Answer 11

Ah, yes, I think you're correct. It's the various event spaces that are needed then.
Yes, silly words and their meanings . . .

Answer 12

number of elements in this sample space is 3
count (or list, then count) the number of numbers that are in the event "divisible by 2, 3 or 5"

Answer 13

*30 not 3!

Answer 14

I'm sure you can take it from here, but I'll add one last hint: also count how many numbers in the set are not divisible by any of 2,3, or 5.