Questions: A box contains four white balls and five black balls. Complete parts (a) and (b) below. Choose the correct tree diagram below. A. B. C. D. The probability of the event that the two balls are of different colors is (Simplify your answer.)

Solution Steps

• The correct tree diagram is option B. This diagram correctly represents the probabilities of drawing two balls of different colors from the box.

• There are two scenarios where the balls drawn are of different colors:
  1. Drawing a white ball first and then a black ball.
  2. Drawing a black ball first and then a white ball.

1. White then Black:

   • Probability of drawing a white ball first: \( \frac{4}{9} \)
   • Probability of drawing a black ball second: \( \frac{5}{8} \)
   • Combined probability: \( \frac{4}{9} \times \frac{5}{8} = \frac{20}{72} = \frac{5}{18} \)

2. Black then White:

   • Probability of drawing a black ball first: \( \frac{5}{9} \)
   • Probability of drawing a white ball second: \( \frac{4}{8} = \frac{1}{2} \)
   • Combined probability: \( \frac{5}{9} \times \frac{1}{2} = \frac{5}{18} \)

• Total probability of drawing two balls of different colors: \[ \frac{5}{18} + \frac{5}{18} = \frac{10}{18} = \frac{5}{9} \]

Final Answer