Multiple choice

A pair of fair dice is tossed. Find the probability that the maximum of the two numbers is greater than $4$.

  1. $\dfrac{5}{9}$
  2. $\dfrac{4}{9}$
  3. $\dfrac{2}{9}$

  4. None of these
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A Correct answer
Explanation

The total outcomes for two dice are 36. The outcomes where the maximum is <= 4 are (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4), which is 16 outcomes. The probability of max <= 4 is 16/36 = 4/9. Therefore, the probability of max > 4 is 1 - 4/9 = 5/9.

AI explanation

The probability that the maximum of the two numbers is greater than 4 is the complement of the probability that both dice show numbers 4 or less. Since the probability of a die showing 4 or less is 4/6, the probability of both dice doing so is 16/36. Subtracting this from 1 gives 20/36, which simplifies to 5/9.

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