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I was confused how to approach this problem. It is provided in the sample paper for mma of isi masters exam of 2021.

Subbhashit Mukherjee
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    @DuncanRamage That is a different question. In that case, you can use symmetry to conclude that the answer is $1/2$. Here, you have to subtract the probability that no roll results in a number higher than $4$ from the probability that no roll results in a number higher than $5$. – N. F. Taussig Apr 30 '22 at 16:40
  • @N.F.Taussig Exactly true. I think I've seen this question before on MSE but I have not been able to find it. – David K Apr 30 '22 at 16:55
  • @DavidK I found this related question. – N. F. Taussig Apr 30 '22 at 17:00

1 Answers1

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The probability the highest number is less than $5$ is $(4 / 6)^5$, since every die roll must be $1, 2, 3,$ or $4$. The probability the highest number is no greater than $5$ is $(5/6)^5$, since every die roll must be $1, 2, 3, 4,$ or $5$. Thus, the probability the highest number is exactly $5$ is $$\left(\frac56\right)^5 - \left(\frac46\right)^5 \;=\; \frac{2101}{7776} \;\approx \;0.27.$$

311411
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Joseph Camacho
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