According to a publisher's records, 20% of the books published break even, 30% lose $1000, 25% lose $10,000, and 25% earn $20,000. When a book is published, what is the expected income for the book?
expected income
= .2(0) + .3(-1000) .25(-10000) + .25(20000)
= 2200
To find the expected income for a book, we need to calculate the weighted average of the possible outcomes based on their respective probabilities.
Given the breakdown of outcomes:
- 20% of books break even (earn $0)
- 30% of books lose $1000
- 25% of books lose $10,000
- 25% of books earn $20,000
To calculate the expected income, we multiply each outcome by its respective probability and sum up the results.
Expected Income =
(0.2 * $0) + (0.3 * -$1000) + (0.25 * -$10,000) + (0.25 * $20,000)
Calculating this expression:
Expected Income = $0 + (-$300) + (-$2,500) + $5,000
Expected Income = -$300 + (-$2,500) + $5,000
Expected Income = -$2,800 + $5,000
Expected Income = $2,200
Hence, the expected income for a published book is $2,200.