Question

A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and two black marbles. If it lands tails, a marble is drawn from Box 2, which contains two white and two black marbles. Find P(black|coin fell tails).

Answer 1

P(black|coin fell tails) = ¼

Explanation:

Since a coin has a head and a tail, then probability of landing tail is;

P(tail) = ½

Now, if it falls tails, a marble is drawn from Box 2, which contains two white and two black marbles.

Thus, probability of getting a black marble is; 2/4 = ½

Thus;

P(black|coin fell tails) = ½ × ½ = ¼