Probability Question Regarding defective chips

**zorro** · December 13th 2009, 05:56 PM

Question : If a box contains 75 good IC chips and 25 defective chips, and 12 chips are selected at random. Find
i) the probability that no chip is defective
ii) the probability that atleast one chip is defective

**Danneedshelp** · December 13th 2009, 07:38 PM

Originally Posted by zorro

Question : If a box contains 75 good IC chips and 25 defective chips, and 12 chips are selected at random. Find
i) the probability that no chip is defective
ii) the probability that atleast one chip is defective

i) You want to probability non of the 12 randomly selected chips are defective. So, the 12 randomly selected chips must be selected from the 75 good chips.

To me, the best solution is to use the hypergeometric distribution function

$ \frac{\left(\begin{array}{cc} 25\\ 0\\ \end{array}\right)\left(\begin{array}{cc} 75\\ 12\\ \end{array}\right)}{\left(\begin{array}{cc} 100\\ 12\\ \end{array}\right)}$

Here is some information on how to use the hypergeometric distribution: http://en.wikipedia.org/wiki/Hyperge...c_distribution.

**zorro** · December 13th 2009, 08:09 PM

Originally Posted by Danneedshelp

i) You want to probability non of the 12 randomly selected chips are defective. So, the 12 randomly selected chips must be selected from the 75 good chips.

To me, the best solution is to use the hypergeometric distribution function

$ \frac{\left(\begin{array}{cc} 25\\ 0\\ \end{array}\right)\left(\begin{array}{cc} 75\\ 12\\ \end{array}\right)}{\left(\begin{array}{cc} 100\\ 12\\ \end{array}\right)}$

Here is some information on how to use the hypergeometric distribution: Hypergeometric distribution - Wikipedia, the free encyclopedia.

Probability of no chips being defective is P(A)
$ P(A) = \frac{\left(\begin{array}{cc} 25\\ 0\\ \end{array}\right)\left(\begin{array}{cc} 75\\ 12\\ \end{array}\right)}{\left(\begin{array}{cc} 100\\ 12\\ \end{array}\right)} = 0.025$ .................Is this correct???

ii) Probability of at least 1 chip being defective

$P(B \ge 1) = 1 - P(A)$ .............am i correct?

**pickslides** · December 13th 2009, 08:25 PM

Originally Posted by zorro

$P(B \ge 1) = 1 - P(A)$ .............am i correct?

Yep

**zorro** · December 13th 2009, 08:31 PM

Originally Posted by pickslides

Yep

Thanks for all ur support guys

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