Question

Of the 750 participants in a professional meeting, 450 are females 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 book prize, what is the probability that the person selected will be less than thirty years old?

• A. \( \frac{1}{8} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{3}{8} \)
• D. \( \frac{2}{5} \)
• E. \( \frac{3}{4} \)

Hint:

To find probability, divide the number of favorable outcomes by the total number of outcomes.

Answer 1

The Correct Option is B

The total number of participants is 750.
- 450 are females.
- Thus, the number of males is \( 750 - 450 = 300 \).
- 1/4 of the male participants are less than thirty years old, so the number of males less than thirty is \( \frac{1}{4} \times 300 = 75 \).
- Half of the females are less than thirty years old, so the number of females less than thirty is \( \frac{1}{2} \times 450 = 225 \).
Thus, the total number of participants under thirty is \( 75 + 225 = 300 \).
The probability is the ratio of participants under thirty to the total participants: \[ P(\text{under 30}) = \frac{300}{750} = \frac{1}{3} \]
Final Answer: \[ \boxed{\frac{1}{3}} \]