An urn contains 8 red, 9 white, and 2 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 at least one ball drawn is black B.
A) Pr(at least one
B) =
B) Pr(at least one
B) =
C) Pr(at least one
B) =
D) Pr(at least one
B) =
E) Pr(at least one
B) =

Question

An urn contains 8 red, 9 white, and 2 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 at least one ball drawn is black B. ​
A) Pr(at least one 
B) = 
B) Pr(at least one 
B) = 
C) Pr(at least one 
B) = 
D) Pr(at least one 
B) = 
E) Pr(at least one 
B) =

Quizplus · Accepted Answer

The probability tree for the given problem is as follows:

R (8/19)      
       /   \       
      R     W
     / \   / \
    R   W R   W
   / \ / \/ \ / \
  R  W R W R W R W
 B B B B B B B B

The probability of getting at least one black ball can be calculated by finding the probability of getting one black ball and the probability of getting two black balls and then adding them.

Probability of getting one black ball = 2/19 (since there are 2 black balls out of 19 total balls)

Probability of getting two black balls = (2/19) x (2/19) = 4/361

Therefore, the probability of getting at least one black ball is:

2/19 + 4/361 = 0.117647

Rounding to three decimal places, we get 0.118.

The closest answer choice to 0.118 is D, with a value of 0.119. Therefore, the best choice is D.

An Urn Contains 8 Red, 9 White, and 2 Black