A bin of $35$ parts contains $6$ defective parts and $29$ non defective parts. The sample size is $5$ and not replaced. What is the probability that a sample contains exactly two defective parts?
What is the probability that a sample contains exactly two defective parts?
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probability
3 Answers
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There are ${5 \choose 2}$ ways to pick the defective parts, and ${29 \choose 3 }$ ways to pick 3 good parts.
The total way we can pick our sample is ${35 \choose 5}$.
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Just calculate straight forward $P(2def.)= \frac{\binom{5}{2} \binom{29}{3}}{\binom{35}{5}}$ where you pick 2 out of five defective parts and 3 out of 29 good parts.
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I feel like I'm doing your homework, BUT,
We know that if you took at piece at random from the bin, there is a $N = \frac{29}{35}$ chance that it's non defective, and a $D = \frac{6}{35}$ chance that it is defective.
- N means non defective
- D means defective
To figure out the probabilty of picking $5$ pieces so that $2$ are defective, and $3$ are non defective, we would multiply $D*D*N*N*N$, and I got the result of $\frac{878004}{52521875}$, which is approximately $0.0167$