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.

Answer 1

number of chips tested before defective one is found?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

yes

Answer 6

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

Answer 7

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

Answer 8

yw