IIT JEE , AIEEE Forum - Mathematics , Algebra - n digits r taken @ random & multiplied then P(last digit is 1,3,7,9),P(l.. 5),P(2,4,6,8)

bhuwanaroracorroded

n digits r taken @ random & multiplied then P(last digit is 1,3,7,9),P(l.. 5),P(2,4,6,8)

bhuwanaroracorroded

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nadeemoidu

Last digit will be 1,3,7,9 if all the nos. are odd and none are divisible by 5.

Last digit will be 5 if all the nos. are odd and atleast one is 5.

Last digit will be 2,4,6,8 if all the nos. are even and none are divisible by 5.

iitkgp_bipin

Possible digits are 0,1,2,3,4,5,6,7,8,9.... total 10 digits.

For last digit to e 1,3,7,9 : all n digits should be odd except 5 i.e. digits can be chosen among 1,3,7,9

so P = (4/10)ⁿ= (2/5)ⁿ

For last digit to be 5 at least one digit should be 5 and others should be odd.

P = ⁿC₁(1/10)(5/10)^n-1

For last digit to be 2,4,6,8 at least one digit should be among 2,4,6,8 and others can be any digit except 0 and 5.

P = ⁿC₁(4/10)(8/10)^n-1

edited : thanks nadeemoidu for correcting.

nadeemoidu

EDIT: the above answer is now correct.

2) For last digit to be 5 at least one digit should be 5 and others should be odd.

Atleast one digit should be 5 means, P(last digit is 5)= ⁿC₁ ( 1/10) ( 5/10) ^n-1= (n/10) ( 5/10) ^n-1

Otherwise , it is like assuming that the first digit is 5.

3)
For last digit to be 2,4,6,8 at least one digit should be among 2,4,6,8 and others can be any digit except 0 and 5.

Again P(last digit is 2,4,6,8) = ⁿC₁ (4/10) ( 8/10)^n-1

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