Multiple choice

A ball is drawn from an urn containing one red ball and one black ball. If the ball drawn is red, a coin is tossed; if it is black, a die is rolled. What is the probability of getting a head?

  1. 1 / 2

  2. 1 / 12

  3. 1 / 4

  4. 1 / 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of picking a red ball is 1/2, and the probability of getting a head from a coin toss is 1/2. The probability of picking a black ball is 1/2, and the probability of getting a head from a die roll is 0. Thus, the total probability is (1/2 * 1/2) + (1/2 * 0) = 1/4.

AI explanation

Using the law of total probability, the overall probability of getting a head is the sum of the probabilities of the two independent paths that result in a head. The probability of drawing a red ball and tossing a head is 1/2 times 1/2, which equals 1/4. The probability of drawing a black ball and rolling a head is zero because a coin is not tossed, so the total probability is 1/4 plus 0, giving a final result of 1/4.

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