Weighted voting by gender split: In an office, 40% of the staff are female and 60% are male. If 40% of the females and 60% of the males voted for me, what percentage of the entire staff voted for me?
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A24%
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B42%
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C50%
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D52%
Answer
Correct Answer: 52%
Explanation
Introduction / Context:This is a weighted average problem across two groups with different sizes and different within-group support rates. We must weight each group’s support by its proportion in the total staff before summing to find the overall support percentage.Given Data / Assumptions:
- Female proportion = 40% of staff.
- Male proportion = 60% of staff.
- Support within females = 40%.
- Support within males = 60%.
Concept / Approach:Overall support = (female share * female support) + (male share * male support). Convert all to decimals and multiply accordingly.
Step-by-Step Solution:
Female contribution = 0.40 * 0.40 = 0.16 (16%).Male contribution = 0.60 * 0.60 = 0.36 (36%).Total support = 0.16 + 0.36 = 0.52 = 52%.Verification / Alternative check:Assume a 100-person office: 40 females → 16 supporters; 60 males → 36 supporters; total = 52 supporters → 52%.
Why Other Options Are Wrong:
- 24%: Counts only female supporters wrongly as overall.
- 42% or 50%: Arithmetic slips or averaging 40% and 60% without weights.
Common Pitfalls:Averaging 40% and 60% to get 50% without weighting by 40% and 60% group sizes. Always apply weighted averages when groups differ in size.
Final Answer:
52%