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?
Show Hint
- \( \frac{1}{8} \)
- \( \frac{1}{3} \)
- \( \frac{3}{8} \)
- \( \frac{2}{5} \)
- \( \frac{3}{4} \)
The Correct Option is B
Solution and Explanation
- 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: \[ \boxed{\frac{1}{3}} \]
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