3 of 10 samples are contaminated. 2 are randomly chosen. What is the probability of both of the chosen samples are contaminated?

Hope you can help.

Thanks.

EDIT:please include all working.

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- Aug 14th 2006, 11:13 PMBartimaeus3 of 10 samples are contaminated
3 of 10 samples are contaminated. 2 are randomly chosen. What is the probability of both of the chosen samples are contaminated?

Hope you can help.

Thanks.

EDIT:please include all working. - Aug 14th 2006, 11:44 PMCaptainBlackQuote:

Originally Posted by**Bartimaeus**

Probability that second sample is contaminate given the first

is contaminated is P2=2/9.

Probability both contaminated=P1*P2

RonL - Aug 15th 2006, 12:10 AMBartimaeus
Thanks RonL

- Aug 15th 2006, 06:22 AMSoroban
Hello, Bartimaeus!

RonL's solution is the best one.

Here's an alternate approach (if you're familiar with Combinations).

Quote:

Three of ten samples are contaminated. .Two are randomly chosen.

What is the probability of both of the chosen samples are contaminated?

There are $\displaystyle \binom{10}{2} = 45$ possible outcomes.

To get two contaminated samples, there are: $\displaystyle \binom{3}{2} = 3$ ways.

Therefore: .$\displaystyle P(\text{both contaminated}) \:=\:\frac{3}{45} \:=\:\frac{1}{15}$

- Aug 23rd 2006, 11:15 PMBartimaeus
I'm not really familiar with Combinations.

Could you explain them further to me, please?

:) - Aug 24th 2006, 11:40 AMThePerfectHackerQuote:

Originally Posted by**Bartimaeus**

.36 .357 .308 .45 .50

And you are told to select two of them, the possibilities are,

Code:`.36 and .357`

.36 and .308

.36 and .45

.36 and .50

.357 and .308

.357 and .45

.357 and .50

.308 and .45

.308 and .50

.45 and .50

You chose 2 from 5. We write,

$\displaystyle {5 \choose 2}=10$ another notation,

$\displaystyle _5C_2=10$.

The mathematical formula is,

$\displaystyle {n\choose m}=\frac{n!}{m!(n-m)!}$

Note: Sometimes the combinations formula is refferred to as the binomial coefficients. Because the coefficients in the binomial expansion follow the combinations formula.