Question

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.

Answer 1

Explanation:

a. The probability of selecting a purple marble on the first draw is 7/9. Since the marble is not replaced, there are 6 purple marbles and 1 white marble left in the bag. The probability of selecting a white marble on the second draw is 2/7. Therefore, the probability of selecting a purple marble and then a white marble is (7/9) * (2/7) = 2/9.

b. The probability of selecting a white marble on the first draw is 2/9. Since the marble is not replaced, there is only 1 white marble left in the bag. The probability of selecting a white marble on the second draw is 1/8. Therefore, the probability of selecting two white marbles is (2/9) * (1/8) = 1/36.

c. To compare the probability of selecting two white marbles in a row and two purple marbles in a row, we need to calculate the probabilities of each event separately. 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 is (7/9) * (6/8) = 21/36, since there are 7 purple marbles and 9 total marbles on the first draw, and then 6 purple marbles and 8 total marbles on the second draw (assuming the first marble was not replaced).

Therefore, there is a greater chance of selecting two purple marbles in a row than two white marbles in a row.

Hope this helped!