Question

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?

a. 1/2
b. 2/5
c. 8/15
d. 9/20

Answer 1

The probability is 9/20. Hence the correct option is d.

1. Identifying Favourable Outcomes:

There are 6 multiples of 3 between 1 and 20: 3, 6, 9, 12, 15, 18.

There are 4 multiples of 5 between 1 and 20: 5, 10, 15, 20.

However, we need to adjust for double counting:

Number 15 is a multiple of both 3 and 5, so it has been counted twice in the previous steps.

Therefore, we need to subtract 1 for this double counting: 6 multiples of 3 + 4 multiples of 5 - 1 double count = 9 favourable outcomes.

2. Total Possible Outcomes:

There are 20 tickets (numbered 1 to 20) in total, so there are 20 possible outcomes when drawing one ticket.

3. Calculating Probability:

The probability of drawing a ticket divisible by 3 or 5 is the number of favourable outcomes divided by the total possible outcomes:

Probability = Favourable Outcomes / Total Possible Outcomes

Probability = 9 / 20

Therefore, the probability of drawing a ticket divisible by 3 or 5 is 9/20. Hence the correct option is d.