Question

Seventy cards are numbered 1 through 70 , one number per card. One card is randomly selected from the deck. What is the probability that the number drawn is a multiple of 3 AND a multiple of 5 ?

Answer 1

`Probability = (2)/(35)`

Explanation:

Given

`Total = 70`

First, we need to list the multiples of 5

`M_5 = \{5,10,15,20,25,30,35,40,45,50,55,60,65,70\}`

Then, multiples of 3
`M_3 = \{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69\}`

Next, is to list out the common elements in both

`M_3\ n\ M_5 = \{15,30,45,60\}`

`n(M_3\ n\ M_5) = 4`

The required probability is then calculated as thus:

`Probability = (n(M_3\ n\ M_5))/(Total)`

`Probability = (4)/(70)`

`Probability = (2)/(35)`