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?

Having in mind that what we need is to find people with less than 30 years old, no matter what gender. So we might proceed like this:
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.
And now what you need to do is to add them like this:
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%
Hope this is good one to you