Answer: 5/14 which is choice B
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How I got this answer:
Define the following events
A = event of picking a red paper clip on the first selection
B = event of picking a red paper clip on the second drawing
Replacement is not made.
Now onto the probabilities for each
P(A) = 2/5 = 0.4 is given to us as this is simply the probability of picking red on the first try
P(A and B) = probability of both events A and B happeing simultaneously = 1/7
P(B|A) = probability event B occurs, given event A has occured
P(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) = 5/14
So if event A happens, then the chances of event B happening is 5/14
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A more concrete example:
If we had 15 paperclips, and 6 of them were red, then
P(A) = (# of red)/(# total) = 6/15 = 2/5
P(B|A) = (# of red left)/(# total left) = (6-1)/(15-1) = 5/14
P(A and B) = P(A)*P(B|A) = (2/5)*(5/14) = 10/70 = 1/7
