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A Dice is Rolled 5 Times. What is the Probability that the Sum of the 5 Numbers Shown is Equal to 25? - Mathematics

MCQ

A Dice is rolled 5 times. What is the probability that the sum of the 5 numbers shown is equal to 25?

Options

  • `210/6^5`

  • `126/6^5`

  • `21/6^5`

  • `7/432`

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Solution

Let abcde is the outcome when dies is rolled 5 times. Now 1 ≤ a, b, c, d, e ≤ 6.
If we try to make cases, it will be a lengthy sum. Let us assume we get (6, 6, 6, 6, 6) all five times. Here the sum is 30 but we want 25. It means there is a drop of 5 in total. So, let us consider the outcome is (6 – x, 6 – y, 6 – z, 6 – p, 6 – r) Where x + y + z + p + r = 5and 0 ≤ x, y, z, p, r≤ 5 & the non-negative integral soln. for this equation are 5+5-1C5-1 = 126.

So probability = `126/6^5`.

Concept: Probability (Entrance Exam)
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