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?

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:

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: