In a scenario with two boxes (one with 1 black and 1 white marble, the other with 2 black and 1 white), what is the probability of picking a black marble?

• A. 0.66
• B. 0.5
• C. 0.583
• D. 0.417

Answer: (C)

To calculate the probability of picking a black marble from the two boxes, we can analyze the situation step by step.

First, let's identify the contents of both boxes:

• Box 1 contains 1 black marble and 1 white marble.

• Box 2 contains 2 black marbles and 1 white marble.

Assuming there is an equal chance of selecting either box, the total probability of drawing a black marble can be obtained by evaluating the outcomes for each box.

1. If you select Box 1:

• The probability of picking a black marble from Box 1 is 1 out of 2 (or 0.5).

2. If you select Box 2:

• The probability of picking a black marble from Box 2 is 2 out of 3 (or approximately 0.6667).

Since each box is equally likely to be chosen, we find the overall probability of selecting a black marble by averaging these probabilities:

• The probability of picking a black marble overall is calculated as:

• P(black | Box 1) × P(Box 1) + P(black | Box 2) × P(Box 2)

• = (0.5 * 0.