Question

Amy has a bag of red, blue, and black pens. she randomly selects a pen, records the color, and puts it back in the bag. she does this a total of 30 times and selects 6 red, 10 blue, and 14 black pens.

based on this information, what is the probability that Amy will select a blue pen, return it to the bag, and than select a red pen?

Answer 1

Since Amy returns the pen to the bag after selecting it, the probability of selecting a blue pen on the first draw is 10/30, or 1/3. The probability of selecting a red pen on the second draw is also 6/30, or 1/5.

Since these two events are independent (the first draw does not affect the second draw), we can multiply the probabilities together to find the probability of both events occurring:

P(blue, then red) = P(blue) × P(red) = (1/3) × (1/5) = 1/15

Therefore, the probability that Amy will select a blue pen, return it to the bag, and then select a red pen is 1/15.