Question

8. A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and one black

marble. If it lands tails, a marble is drawn from Box 2, which contains two white and one black marble. Find:
a) P (black coin fell heads)
b) P (white coin fell tails)

Answer 1

a) 0.25

b) 0.34

Explanation:

There are two levels of probability to consider; the probability of the coin being heads or tails, and after that the probability of choosing a white or black marble (depending on which box is chosen).

The probability of heads is 0.5 and the probability of tails is 0.5.

For Box 1 (i.e. coin was heads), the probability of choosing a white marble is 0.5, and the probability of choosing a black marble is 0.5.

For Box 2 (i.e. coin was tails), the probability of choosing a white marble is 0.67, and the probability of choosing a blck marble is 0.33.

The probability that the coin fell heads AND the marble is black is 0.5 x 0.5 = 0.25

The probability that the coin fell tells AND the marble is white is 0.5 x 0.67 = 0.34.

Remember, "and" means multiply probabilities (for independent events).