Question

A bag contains 50 lotteryballs, numbered 1-50. A ball ischosen at random, then a monthof the year is selected. What isthe probability of choosing amultiple of 3 and a monthstarting with the letter "M"?

Answer 1

`(4)/(75)`

1) As always, the best way to solve a probability problem is by finding the sample space.

In this case, there are 50 lottery balls from 1 to 50 and 12 months.

2) Now, the next part is to find the favorable events

Multiple of 3 from 1-50

`\lbrace3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48\rbrace`

So there are 16 elements from the favorable event set

`\lbrace march,\:may\rbrace`

2 months out of 12

3) Note that the question says the Probability of picking a multiple of 3 out of those 50 lottery balls And choosing one month whose first letter is M

So, let's find our probability:

`P=(16)/(50)*(2)/(12)=(32)/(600)=(4)/(75)`

Thus, the answer is:

`(4)/(75)`