# Binomial Distribution Probability

## Homework Statement

A quality control engineer tests the quality of produced computers. Suppose that 5% of computers have defects, and defects occur independently of each other.

A- What is the expected number of defective computers in a shipment of twenty?
B- Find the probability of exactly 3 defective computers in a shipment of twenty.
C- Find the probability that the engineer has to test at least 5 computers in order to find a defective one.

## The Attempt at a Solution

A-1
B- .061 which were correct

For C I got .00257 which was wrong. I just don't understand how I'm supposed to find at least 5 when I don't know the total number since for finding .00257 I used n=20 which I guess I wasn't supposed to since I got it wrong

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tiny-tim
Homework Helper
hi lina29!
Suppose that 5% of computers have defects, and defects occur independently of each other.

C- Find the probability that the engineer has to test at least 5 computers in order to find a defective one.
with questions like this, it often helps to write out the opposite, and find the probability of that

so how would you write (in english) the opposite of "the engineer has to test at least 5 computers in order to find a defective one" ?

the engineer has to test at most 4 computers in order to find a defective one

tiny-tim
Homework Helper
oops!

oops!

yes, that's right, i asked the wrong question

i should have asked you just to rewrite the question in terms of successes, rather than failures

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

A quality control engineer tests the quality of produced computers. Suppose that 5% of computers have defects, and defects occur independently of each other.

A- What is the expected number of defective computers in a shipment of twenty?
B- Find the probability of exactly 3 defective computers in a shipment of twenty.
C- Find the probability that the engineer has to test at least 5 computers in order to find a defective one.

## The Attempt at a Solution

A-1
B- .061 which were correct

For C I got .00257 which was wrong. I just don't understand how I'm supposed to find at least 5 when I don't know the total number since for finding .00257 I used n=20 which I guess I wasn't supposed to since I got it wrong
Please show your work. Where, exactly, does the number 0.00257 come from? Without this information it is impossible to help you; we cannot tell if you used the correct formula but made an arithmetical error, or what.

RGV

using my calculator I did 1-binomcdf(20,.05,4)

I don't know how I would write it in terms of successes rather than failures

tiny-tim
Homework Helper
C- Find the probability that the engineer has to test at least 5 computers in order to find a defective one.
so how many good ones will there be?

15? assuming that C also is also doing a shipment of 20 computers. So would I find exactly 15 successes?

tiny-tim
Homework Helper
C- Find the probability that the engineer has to test at least 5 computers in order to find a defective one.
if he gets to the 5th computer, what happened to the first 4 ?

they were nondefective

tiny-tim
Homework Helper
yes!

so probability that the engineer has to test at least 5 computers in order to find a defective one = probability that the first 4 are not defective

which is … ?

(.95)^4=.81451

tiny-tim