Question

Tickets numbered 1 through 20 are in a bag. What's the probability of picking a number that is a multiple of either 3 or 5?

Answer 1

`P("multiple of 3 or 5")=9/20`

Explanation:

The probability is a ratio - the numerator of those numbers that meet the condition (multiple of 3 or 5) divided by the number of tickets it's possible to pick from (20).

The numbers that are a multiple of 3 or 5 are:

`3, 5, 6, 9, 10, 12, 15, 18, 20`, which is 9 numbers.

This gives:

`P("multiple of 3 or 5")=9/20`

Answer 2

Probability of (multiple of 3 or 5)`=9/20`

Explanation:

Probability of (multiple of 3 or 5) = Probability of (multiple of 3 ) + Probability of (multiple of 5)

Probability of a simple event is =Number of favourable events `-:`Total Number of Events.

Probability of (multiple of 3 )

Total Number of events = 20
Number of favourable events [3,6,9,12,15,18] = 6

Probability of (multiple of 3 )`=6/20=3/10`

Total Number of events = 20
Number of favourable events [5,10,15,20] = 4

Probability of (multiple of 5) `= 4/20=1/5`

Number 15 occurs two times. One time occurrence must be deducted.

Probability of occurring 15 one time`=1/20`

Probability of (multiple of 3 or 5) = Probability of (multiple of 3 ) + Probability of (multiple of 5) - Probability of occurring 15 one time

Probability of (multiple of 3 or 5)`=3/10+1/5-1/20=(6+4-1)/20=9/20`