4 dices are thrown simultaneously. What is the probability that all the dices show the same number
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let n(t) be the total number of out comes:
n(t) = 6*6*6*6 =6^4
now let n(f) be the favourable number of outcomes showing the same number that is {(1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}
n(f)=6
hence probability required = favourable possibilities divided by total possibilities = n(f)/n(t) = 6/6^4= 1/216
n(t) = 6*6*6*6 =6^4
now let n(f) be the favourable number of outcomes showing the same number that is {(1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}
n(f)=6
hence probability required = favourable possibilities divided by total possibilities = n(f)/n(t) = 6/6^4= 1/216
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