A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.
a. What is the probability of selecting a purple marble and then a white marble?
b. What is the probability of selecting two white marbles?
c. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row? Show your work.
a. The probability of selecting a purple marble on the first draw is 7/9. After one purple marble is drawn and not replaced, there are now 2 white marbles and 6 purple marbles left. The probability of selecting a white marble on the second draw is 2/8 or 1/4. The overall probability of selecting a purple marble and then a white marble is (7/9) * (1/4) = 7/36.
b. The probability of selecting a white marble on the first draw is 2/9. After one white marble is drawn and not replaced, there is only 1 white marble left in the bag. The probability of selecting another white marble on the second draw is 1/8. The overall probability of selecting two white marbles is (2/9) * (1/8) = 1/36.
c. To determine which outcome has a greater chance, we compare the probability of selecting two white marbles to the probability of selecting two purple marbles.
For two white marbles in a row, the probability is 1/36.
For two purple marbles in a row, the probability can be calculated as follows: The probability of selecting a purple marble on the first draw is 7/9. After one purple marble is drawn and not replaced, there are now 6 purple marbles left in the bag. The probability of selecting another purple marble on the second draw is 6/8 or 3/4. The overall probability of selecting two purple marbles in a row is (7/9) * (3/4) = 21/36.
Therefore, there is a greater chance of selecting two purple marbles in a row (21/36 > 1/36).