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! .
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.
|
|
|
