Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order.
A) Pr(two W ∩ one
R) =
B) Pr(two W ∩ one
R) =
C) Pr(two W ∩ one
R) =
D) Pr(two W ∩ one
R) =
E) Pr(two W ∩ one
R) =

Question

Three balls are drawn, without replacement, from a bag containing 9 red balls and 7 white balls. Construct a probability tree to determine the probability that two white W balls and one red R ball are drawn in any order. ​
A) Pr(two W ∩ one 
R) = 
B) Pr(two W ∩ one 
R) = 
C) Pr(two W ∩ one 
R) = 
D) Pr(two W ∩ one 
R) = 
E) Pr(two W ∩ one 
R) =

Quizplus · Accepted Answer

The probability tree is as follows:

R (9/16)
         /   \
        W   W (7/15)(6/14)
       /     \
      W      W (7/15)(5/14)
     /         \
    W          W (6/15)(5/14)

The probability of getting two white balls and one red ball in any order is the sum of the probabilities of getting RWW, WRW, and WWR.

RWW has a probability of (9/16) x (7/15) x (6/14) = 21/160

WRW has a probability of (9/16) x (7/15) x (6/14) = 21/160

WWR has a probability of (7/16) x (6/15) x (9/14) = 21/160

Adding these probabilities together gives 63/160, which is choice (B).

Three Balls Are Drawn, Without Replacement, from a Bag Containing