Problem 10 · Weighted conditional probability · 5 points
Made by AI and not reviewed by a real person.
Three points are picked independently and uniformly from inside the pie chart. Given that they land in three different slices, what is the probability that one lands in books?
- 88%
- 78.4%
- 40%
- 75%
- 90%
Show a hint
- Three different slices leave exactly one slice out. Are the four possible missing slices equally likely?
- For each possible missing slice, multiply the percentages of the three slices that remain. Each group of three can occur in the same number of orders.
Show the answer and solution
Answer: A — 88%
The four groups of three slices have relative weights 40×30×20, 40×30×10, 40×20×10, and 30×20×10. Their total is 50,000; the group without books has weight 6,000. So the probability is 1 − 6,000/50,000 = 88%. The tempting 75% treats the four possible missing slices as equally likely, but their weights differ.