A cup of pens contains 5 red, 12 black, and 13 blue pens. A pen is chosen randomly and not replace. Then a second pen chosen. What is the probability that the first pen is black and the second pen is red? Would the correct answer be 2/29?
correct
To determine the probability of drawing a black pen first and then a red pen, we need to find the individual probabilities for each event and then multiply them together.
First, let's find the probability of drawing a black pen first. We have a total of 5 red pens, 12 black pens, and 13 blue pens, making a total of 5 + 12 + 13 = 30 pens. The probability of choosing a black pen on the first draw is 12/30.
Now, since we don't replace the first pen, there are 29 pens left in the cup for the second draw. However, after the first pen is drawn, the total number of black pens decreases by 1 to 11, and the total number of pens decreases to 29.
To find the probability of drawing a red pen second, we now have 5 red pens and 29 pens in total. Therefore, the probability of choosing a red pen on the second draw, given that a black pen was chosen first, is 5/29.
To calculate the overall probability, we multiply the individual probabilities together:
(12/30) * (5/29) = 60/870 = 2/29
So, yes, the correct answer is indeed 2/29.