An urn contains 7 red, 3 white, and 6 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that one ball is white W and one is red R.
A) Pr(one W ∩ one
R) =
B) Pr(one W ∩ one
R) =
C) Pr(one W ∩ one
R) =
D) Pr(one W ∩ one
R) =
E) Pr(one W ∩ one
R) =

Question

An urn contains 7 red, 3 white, and 6 black balls. One ball is drawn from the urn, it is replaced, and a second ball is drawn. Construct a probability tree to determine the probability that one ball is white W and one is red R. ​
A) Pr(one W ∩ one 
R) = 
B) Pr(one W ∩ one 
R) = 
C) Pr(one W ∩ one 
R) = 
D) Pr(one W ∩ one 
R) = 
E) Pr(one W ∩ one 
R) =

Quizplus · Accepted Answer

The probability tree for the given scenario would look like this:

R          W          B
           /     \     /     \     /    \
          R      W     B     R    W    B
         / \    /  \  / \   / \   / \  / \
        R  W  R   W B  R W   R  W  B R  W

The probability of selecting a white ball on the first draw is 3/16, and the probability of selecting a red ball on the second draw is also 7/16. The probability of selecting a red ball on the first draw is 7/16, and the probability of selecting a white ball on the second draw is 3/16.

To calculate the probability of getting one white ball and one red ball, we can add the probabilities of the two possible outcomes:

(3/16) * (7/16) + (7/16) * (3/16) = 42/256

Simplifying, we get:

42/256 = 21/128

Therefore, the correct choice is C.

An Urn Contains 7 Red, 3 White, and 6 Black