Tickets numbered from one to 40 are mixed up and one is drawn.

Question

What is the probability that number is divisible by 3 or 5?
What is the probability that number is divisible by 3 and 5?

Answer 1

x: How many multiples of 3 are there in 1-40?
y: How many multiples of 5?
z: how many multiples of 15?
P(x or y) = (x+y-z)/40
P(x and y) = P(z) = z/40

Answer 2

8/40+13/40-2/40 =19/40

8/40 numbers divisible by 5
13/40 numbers divisible by 3
2/40 overlapping numbers which are 15 and 30

Answer 3

n = 40
n(A) = 13+8-2 = 21-2
⇒ P(A) = 19/40

Answer 4

Yes, that is correct for the probability that the number drawn is divisible by 3 or 5.

For the probability that the number is divisible by 3 and 5, we need to find the number of multiples of 15 in the range of 1 to 40.

Multiples of 15 are: 15, 30. So, there are 2 multiples of 15 in the range of 1 to 40.

Therefore, the probability that the number drawn is divisible by both 3 and 5 (i.e., by 15) is:

P(B) = 2/40

Alternatively, we can use the formula for the probability of the intersection of two events:

P(A ∩ B) = P(A) × P(B|A)

Here, P(A) is the probability of the event that the number is divisible by 3, which is 13/40.

The probability of the event that the number is divisible by 5, given that it is already known to be divisible by 3 (i.e., given the event A), is 2/13, because the only multiples of 5 that are also multiples of 3 are 15 and 30.

So, we can calculate P(B) as:

P(B) = P(A ∩ B) / P(A|B) = (13/40) × (2/13) = 2/40

Either way, we get the same answer: P(B) = 2/40 = 1/20.