Multiple choice

An die is tossed twice. Find the probability of getting $4,5\ or\ 6$ on the toss and $1,2,3\ or\ 4$ on the second toss.

  1. $\dfrac 13$
  2. $\dfrac 23$
  3. $\dfrac 34$
  4. $\dfrac 12$
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A Correct answer
Explanation

The probability of getting 4, 5, or 6 on one die is 3/6 = 1/2. The probability of getting 1, 2, 3, or 4 on the second die is 4/6 = 2/3. Since the events are independent, the joint probability is (1/2) * (2/3) = 1/3.

AI explanation

Using the multiplication theorem of probability for independent events, the probability is the product of the individual probabilities. The probability of getting 4, 5, or 6 on the first toss is 3/6, and the probability of getting 1, 2, 3, or 4 on the second toss is 4/6. Multiplying these gives (3/6) times (4/6), which equals 12/36 or 1/3. The probability is 1/3.

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