# Probability question

A factory worker places 86 newly created circuits on a shelf to be checked for quality. Of these 6 will not work correctly. Suppose that she is asked to randomly select two circuits, without replacement, from the shelf. What is the chance that both circuits that she selects will be defective? Show step by step work! Approximate the solution to the nearest ten thousandth.

Answer

There are 6 faulty circuits among 86 in total. The probability of drawing a first faulty circuit is P1 =6/86. Now it remains only 85 circuits and from these only 5 are wrong. The probability of drawing a second faulty circuit is therefore P2 =5/85. The total probability is

P =P1*P2 =6*5/86/85 =0.0041