SOLUTION: An unbiased dice with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum value is not less than 2 and maximu

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Question 1192391: An unbiased dice with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum value is not less than 2 and maximum value is not greater than 5 is
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
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An unbiased dice with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times.
Out of four face values obtained, the probability that the minimum value
is not less than 2 and maximum value is not greater than 5 is
~~~~~~~~~~~~~~~~~


                "dice"  is plural;  a  "single"  form  is  "die".

                "unbiased dice"  in this post means  "fair die".


In the problem's formulation, 


    " the minimum value is not less than 2 and maximum value is not greater than 5"


means that all upper-face values are between 2 and 5,  i.e. are from the interval [2,3,4,5].


For each individual rolling, the probability to have the upper-face value in this interval is  = .


So, we have the binomial distribution experiment with the number of trials 4; the probability of successful trial of 2/3
and the complement probability of unsuccessful trial of  1/3.


Hence, the probability under the problem's question  is

    P =  =  = 0.197531   (rounded).    ANSWER

Solved.



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