Answer to Question #259749 in Statistics and Probability for rtf

Question

Four microprocessors are randomly selected from a lot of 100 microprocessors among which 10 are defective. Find the probability of obtaining no defective microprocessors.

Answer 1

The probability of obtaining no defective microproccessors is equal to probability that every obtained microprocessor is good

Let A be "all microprocessors are good", $A{\scriptscriptstyle n}$ be "n-th microprocessors is good", then

$P(A{\scriptscriptstyle 1})= {\frac {90} {100}}$

$P(A{\scriptscriptstyle 2})= {\frac {89} {99}}$

$P(A{\scriptscriptstyle 3})= {\frac {88} {98}}$

$P(A{\scriptscriptstyle 4})= {\frac {87} {97}}$

Since all probabilities were calculated considering the changes in the amount of the detais after each pick, then

$P(A) =P(A{\scriptscriptstyle 1})*P(A{\scriptscriptstyle 2})*P(A{\scriptscriptstyle 3})*P(A{\scriptscriptstyle 4})={\frac {90*89*88*87} {100*99*98*97}}=0.6516$ (approximately)