Math Is Fun Forum

karney

Guest

probability problem

A test shows that 10 out of 100 gadgets are defective.  If a random sample of two gadgets are chosen, the probability that both are defective is?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: probability problem

(10/100)² = 0.01 = 1%

---

Why did the vector cross the road?
It wanted to be normal.

karney

Guest

Re: probability problem

The study guide I'm using says the answer to this one is 1/110, so I guess I'm confused.  I also thought this woud be 1/10 X 1/10 = 1/100 = 1%

Avon

Member

Registered: 2007-06-28

Posts: 80

Re: probability problem

If the first sentence means "There are 100 gadgets. 10 are defective." then the answer is

karney

Guest

Re: probability problem

Gotcha!  Thanks to all of you.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: probability problem

The first answer (1%) is true if you are taking from a large population (say randomly sampling from your production run)

The second answer (1/110) is true if you are selecting from exactly 100 gadgets, and not replacing.

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

JoAnnI

Guest

Re: probability problem

I still really don't understand why it is 1/110.  Please help.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: probability problem

Hi JoAnni;

MathsisFun's is with replacement and Avon's is without replacement.

Avon's post(# 4) is explained like this:

There are 10 bad picks out of the total 100 for the first choice:
after that there are 9 bad picks left out of 99 total picks for the second choice.
Now you just multiply 10/100 * 9/99 = 1/10 *1/11 = 1/110

Last edited by bobbym (2009-06-04 13:53:31)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.