- #1

- 224

- 7

## Homework Statement

There are 5 errors, and 3 people are proofreading the text.

- P(1. person finds an error) = 0,5
- P(2. person finds an error) = 0,6
- P(3. person finds an error) = 0,7

## Homework Equations

P(A and B) = P(A) * P(B)

## The Attempt at a Solution

Now, my head is telling me, that there are a huge number of ways (combinations) the people could find the errors in. e.g.:

- Person 1 finds all errors, the other 2 find none. (0,5^5 * 0,4^5 * 0,3^5)
- Person 1 finds 3, person 2 finds 1 and person 3 finds 1. ((0,5^3 * 0,5^2 ) * (0,6 * 0,4^4 ) * (0,7 * 0,3^4 )
- Person 1 finds none, person 2 finds 3 and person 3 finds 2. (0,5^5 * (0,6^3 * 0,4^2 ) * (0,7^2 * 0,3^3 ))
- All people find all errors. (= 0,5^5 * 0,6^5 * 0,7^5 )

There is also the issue of possibly having to consider the order in which the errors are found in, but I very much doubt that is required. That would probably really bloat the answer to unreasonable proportions, and I wouldn't know if that's even possible mathematically.

**For the record, the answer at the back of the book is 0,74. This leads me to think that addition is necessary, since probabilities are always 0 <= P <= 1 and the largest probability of finding an error is less than the answer.**