Publishers records state:
20% of books published break even.
30% lose $1000.
25% lose $10,000.
25% earn 20,000.
When a book is published, what is the expected income for the book?
To find the expected income for a book, we need to calculate the weighted average of the incomes based on the probability distribution.
Given the income distribution for books:
20% break even (income = $0)
30% lose $1000
25% lose $10,000
25% earn $20,000
Let's calculate the expected income step-by-step:
1. Calculate the expected income for the 20% of books that break even:
Expected income for break-even books = (20% x $0) = $0
2. Calculate the expected income for the 30% of books that lose $1000:
Expected income for books losing $1000 = (30% x -$1000) = -$300
3. Calculate the expected income for the 25% of books that lose $10,000:
Expected income for books losing $10,000 = (25% x -$10,000) = -$2,500
4. Calculate the expected income for the 25% of books that earn $20,000:
Expected income for books earning $20,000 = (25% x $20,000) = $5,000
5. Sum up all the expected incomes to find the total expected income:
Total expected income = $0 + (-$300) + (-$2,500) + $5,000
= $2,200
Therefore, the expected income for a book when it is published is $2,200.