a. The probability of selecting a purple marble is 7/9, since there are 7 purple marbles out of 9 total. After selecting a purple marble, there are now 1 white marble and 7 purple marbles left in the bag. The probability of selecting a white marble from this reduced set is 1/8. Therefore, the probability of selecting a purple marble and then a white marble is (7/9) x (1/8) = 7/72.
b. The probability of selecting a white marble on the first draw is 2/9. After selecting a white marble and not replacing it, there is now 1 white marble and 7 purple marbles left in the bag. The probability of selecting a white marble from this reduced set is 1/8. Therefore, the probability of selecting two white marbles is (2/9) x (1/8) = 1/36.
c. The probability of selecting two white marbles in a row is 1/36, as calculated in part (b). The probability of selecting two purple marbles in a row can be calculated as follows: the probability of selecting a purple marble on the first draw is 7/9. After selecting a purple marble and not replacing it, there are now 6 purple marbles left in the bag out of a total of 8 remaining marbles. Therefore, the probability of selecting another purple marble is 6/8 = 3/4. The probability of selecting two purple marbles in a row is (7/9) x (3/4) = 21/36. Since 21/36 is greater than 1/36, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.
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. Make sure you answer each question in as few steps as possible
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