Probability: It is known that there is a defective chip on a computer board that contains eight chips. A technician tests the chips one at a time until the defective chip is found. Assume the chip to be tested is selected at random without replacement. Let the random variable X denote the number of chips tested. Find the probability mass function of X.

Question

Probability: It is known that there is a defective chip on a computer board that contains eight chips.  A technician tests the chips one at a time until the defective chip is found.  Assume the chip to be tested is selected at random without replacement.  Let the random variable X denote the number of chips tested.  Find the probability mass function of X.

anonymous · Answer

number of chips tested before defective one is found?

anonymous · Answer

$P(x=1)=\frac{1}{8}$
$$P(x=2)=\frac{7}{8}\times \frac{1}{7}=\frac{1}{8}$$ reasoning that first one was not defective, and second one was defective

anonymous · Answer

didn't say...I typed it verbatim from the book

anonymous · Answer

$$P(x=3)=\frac{7}{8}\times \frac{6}{7}\times \frac{1}{6}=\frac{1}{8}$$ and we see the pattern

anonymous · Answer

yes

anonymous · Answer

hope the reasoning is clear. so the probability you have to test any number between 1 and 8 to find the defective one is $\frac{1}{8}$

anonymous · Answer

yes.....this makes more sense than my initial reasoning.  Thanks so much

anonymous · Answer

yw