if four positive integers are taken and at random and multiplied together,then the probability that the last digit is 1,3,7 or 9 is

dear pankaj,

last digit of product will be 1,2,3,4,5,6,7,8or9 & only if each of the n positive integers ends in any of these integers.now probablity of integer ending with 1,2,3,4,5,6,7,8,or9 is 8/10or4/5 therefore probablity that last digit of the product of n integers is 1,2,3,4, 5,6,7,8,9 is (4/5)ⁿ .next the last digit will be 1,3,7,9 & if only if each of positive integers ends with 1,3,7,or9.the probablity of an integer to end in 1,3,7,9 is 2/5.

therefore probablity or the product of n positive integers end in 1,3,7,9 is (2/5)ⁿ

hence probablity of required event is (4/5)ⁿ -(2/5)ⁿ

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