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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. To find the probability of selecting a purple marble and then a white marble, we need to find the probability of each event and then multiply those probabilities together. The probability of selecting a purple marble on the first draw is 7/9 (since there are 7 purple marbles and a total of 9 marbles). After drawing a purple marble, there is 1 white marble and 6 purple marbles remaining, for a total of 8 marbles. The probability of drawing a white marble on the second draw is 2/8 which simplifies to 1/4. So the probability of drawing a purple marble and then a white marble is (7/9) * (1/4) = 7/36.
b. To find the probability of selecting two white marbles, we need to find the probability of selecting a white marble on the first draw and then another white marble on the second draw. The probability of selecting a white marble on the first draw is 2/9 (since there are 2 white marbles and 9 total marbles). After drawing a white marble, there is 1 white marble and 7 purple marbles remaining, for a total of 8 marbles. The probability of drawing a white marble on the second draw is 1/8. So the probability of drawing two white marbles is (2/9) * (1/8) = 1/36.
c. To find which event has a greater chance, we need to find the probability of selecting two purple marbles in a row. The probability of selecting a purple marble on the first draw is 7/9. After drawing a purple marble, there is 1 white marble and 6 purple marbles remaining, for a total of 8 marbles. The probability of drawing a purple marble on the second draw is 6/8 which simplifies to 3/4. So the probability of drawing two purple marbles is (7/9) * (3/4) = 21/36. Since 21/36 > 1/36, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.