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

a) Adding the marbles together there are 9 total.
The chance of selecting a purple marble, since there are 7, is 7/9
Assuming the purple marble isn't replaced, then selecting a white (2) would be 2/8, or 1/4 chance.

Answer 2

a. The probability of selecting a purple marble on the first draw is 7/9. Since one marble is drawn and not replaced, there are now 8 marbles left in the bag, including 2 white marbles. Therefore, the probability of selecting a white marble on the second draw is 2/8 or 1/4. To find the probability of both events happening, we multiply the probabilities:

(7/9) * (1/4) = 7/36

Therefore, the probability of selecting a purple marble and then a white marble is 7/36.

b. The probability of selecting a white marble on the first draw is 2/9. Since one marble is drawn and not replaced, there are now 8 marbles left in the bag, including 1 white marble. Therefore, the probability of selecting a white marble on the second draw is 1/8. To find the probability of both events happening, we multiply the probabilities:

(2/9) * (1/8) = 1/36

Therefore, the probability of selecting two white marbles is 1/36.

c. To determine whether there is a greater chance of selecting two white marbles in a row or two purple marbles in a row, we compare the probabilities we found in parts (a) and (b). Since 7/36 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.