The diagram below shows the contents of a jar from which you select marbles at random.
a. What is the probability of selecting a red marble, replacing it, and then selecting a blue marble? Show your work.
b. What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? Show your work.
c. Are the answers to parts (a) and (b) the same? Why or why not?
a. The probability of selecting a red marble on the first draw is 6/20, as there are 6 red marbles out of 20 total marbles. Since the marble is replaced, the probability of selecting a blue marble on the second draw is also 6/20. Therefore, the probability of selecting a red marble, replacing it, and then selecting a blue marble is (6/20)*(6/20) = 9/100.
b. The probability of selecting a red marble on the first draw is still 6/20. However, since the marble is not replaced, there are now only 19 marbles left in the jar, and only 5 of them are blue. Therefore, the probability of selecting a blue marble on the second draw, given that a red marble was already selected and removed, is 5/19. Therefore, the probability of selecting a red marble, setting it aside, and then selecting a blue marble is (6/20)*(5/19) = 3/38.
c. No, the answers to parts (a) and (b) are not the same. This is because in part (a), the probability of selecting a blue marble on the second draw is the same as the probability of selecting a blue marble on the first draw, since the marble is replaced. However, in part (b), the probability of selecting a blue marble on the second draw is lower, since a marble (the red one) has already been selected and removed from the jar.