Explanation
This problem can be solved using the conditional probability formula or Bayes' Theorem.
1. Define the variables:
Ratio of men to women = 3:4.
Let the total number of students be 700 for simplicity (since 3+4=7).
Number of men (M) = 300
Number of women (W) = 400
2. Calculate the number of students over 6 feet tall:
3. Total number of students over 6 feet tall:
4. Probability that the selected student is a woman:
We want to find the probability that a student is a woman given that they are over 6 feet tall (W | >6ft):
P(W | >6ft) = \frac{\text{Number of women over 6ft}}{\text{Total students over 6ft}}
P(W | >6ft) = \frac{16}{43}
Conclusion:
The probability that the student is a woman, given they are over six feet tall, is 16/43. The correct option is (c).
