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

$\frac{4}{75}$

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:

$P=\frac{16}{50}\times\frac{2}{12}=\frac{32}{600}=\frac{4}{75}$

Thus, the answer is:

$\frac{4}{75}$