# Aptitude - Probability - Discussion

Discussion Forum : Probability - General Questions (Q.No. 1)
1.
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
 1 2
 2 5
 8 15
 9 20
Explanation:

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

 P(E) = n(E) = 9 . n(S) 20

Discussion:
106 comments Page 3 of 11.

Praveen Kumar Gautam said:   1 decade ago
Answer will be 9/20, because 15 already be considered, so it can not be consider next time. So Sundar & Manju thought wrong.

A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it
hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center
of the circle than the periphery?

a) 0.75 b) 1 c) 0.5 d) 0.25

Hi Guys ..
according to me the answer is 2/5
A = multiple of 3
B = multiple of 5
P(A U B) = P(A) + P(B) - P(A n B)
n(A) = 6 ( 3,6,9,12,15,18)
n(B) = 3 (5,10,15)
n (A n B) = 1 (15 --> this comes in both)
Hence, prob = 6/20 + 3/20 - 1/20 = 8/20 = 2/5

Hi @pawan,
so n(B)={5,10,15,20}
then P(B)=4/20
Hence P(AUB)=6/20+4/20-1/20=9/20.

Yes, answer is 9/20. We should not consider a number more than one time (15 is a multiple of 3 and 5. So, it cannot be used more than once)

Satyendra Shukla said:   1 decade ago
Answer will be 9/20, because 15 already be considered, so it can not be consider next time.

Dharmesh Patel said:   1 decade ago
Yes answer is Only and only 9/20.

The answer is 1/2 because if there is same number we should include it. This not union or intersection model.

Thanks sneha. Ans is 9/20.