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.
in general, the probability of some event
= number of times that event can happen/total number of possible outcomes
you have 2 white and 7 purple
prob of purple = 7/9
prob of white = 2/8 , there are only 8 left since you drew one already.
prob(purple, then white) = (7/9)(2/4) = 7/36
prob(2 whites) = (2/9)(1/8) = 1/36
prob(2 purples) = 7/9(6/8) = 7/12
and of course 7/12 > 1/36
clearly , since you had more purples than whites, the chances of getting purples would be greater than the chances of getting whites.