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? Explain
A. The probability of selecting a purple marble on the first draw is 7/9. Since this marble is not replaced, there are now 1 white marble and 7 purple marbles left in the bag. Therefore, the probability of selecting a white marble on the second draw is 1/8. Multiplying these probabilities together, we get:
(7/9) x (1/8) = 7/72
So the probability of selecting a purple marble and then a white marble is 7/72.
B. The probability of selecting a white marble on the first draw is 2/9. If this marble is not replaced, there is now only 1 white marble left in the bag. Therefore, the probability of selecting another white marble on the second draw is 1/8. Multiplying these probabilities together, we get:
(2/9) x (1/8) = 1/36
So the probability of selecting two white marbles is 1/36.
C. There is a greater chance of selecting two purple marbles in a row. This is because there are more purple marbles in the bag than white marbles. Specifically, there is a 7/9 chance of selecting a purple marble on the first draw, and if this happens, there is a 6/8 chance of selecting another purple marble on the second draw (since one purple marble has already been removed). Multiplying these probabilities together, we get:
(7/9) x (6/8) = 21/36
So the probability of selecting two purple marbles in a row is 21/36, which is greater than the probability of selecting two white marbles (1/36).