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)

a) 0.25

b) 0.34

Step-by-step 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).

what

step-by-step explanation:

a and d