Question

Of the 750 participants in a professional meeting,
450 are female and
1
2
of the female and
1
4
of the
male participants are less than thirty years old. If
one of the participants will be randomly selected to
receive a prize, what is the probability that the
person selected will be less than thirty years old?

Answer 1

2/5

Answer 2

Since all we need is to get somebody less than thirty year old, we don't really care what gender they are, so all we have to do is figure out how many of the 750 participants are less than 30 years old...

450 of them are female, and
1/2 of the females are less than 30 years old
Half of 450 is 225, that makes 225 participants younger than thirty years ...

On to the males... if 450 are females, then 300 are males (assuming you only have two genders of course ;) )
1/4 of the males are younger than thirty years and
A quarter of 300 is 75, that makes 75 more participants younger than thirty years.

Add them up, 225 + 75 = 300 participants younger than thirty years...
The chance therefore of getting somebody younger than thirty is
300/750, or 2/5
or 40%

Answer 3

There are 225 females under the age of 30 and 75 of the 300 males are under 30 so

you have a total of 300 participants under the age of 30. so...

300/750 = 2/5