A box contains different colored paper clips. The probability of drawing two red paper clips from the box without replacement is 1/7 , and the probability of drawing one red paper clip is 2/5 . What is the probability of drawing a second red paper clip, given that the first paper clip is red? 2/35 1/6 2/3 5/14

Accepted Solution

Answer: 5/14 which is choice B================================================How I got this answer:Define the following eventsA = event of picking a red paper clip on the first selectionB = event of picking a red paper clip on the second drawingReplacement is not made.Now onto the probabilities for eachP(A) = 2/5 = 0.4 is given to us as this is simply the probability of picking red on the first tryP(A and B) = probability of both events A and B happeing simultaneously = 1/7P(B|A) = probability event B occurs, given event A has occuredP(B|A) = probability of selecting red on second selection, given first selection is red (no replacement)P(B|A) = P(A and B)/P(A)P(B|A) = (1/7) / (2/5)P(B|A) = (1/7) * (5/2)P(B|A) = (1*5)/(7*2)P(B|A) = 5/14So if event A happens, then the chances of event B happening is 5/14------------------A more concrete example: If we had 15 paperclips, and 6 of them were red, thenP(A) = (# of red)/(# total) = 6/15 = 2/5P(B|A) = (# of red left)/(# total left) = (6-1)/(15-1) = 5/14P(A and B) = P(A)*P(B|A) = (2/5)*(5/14) = 10/70 = 1/7