13/10
Let a=33n where n ε N.If exponent n is chosen at random,find the probabality that units digit of a is 9
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8 Answers
1y no ?
i felt 3/10
coz if u coniser n frm 1 to 10
tehn for 3 values of n u get unit plce 9
y is thsi wrng
??
1yeah gt dat silly me
c
if u consider values of n then
for n=2,6,10,14..u egt 9 in units plce
so itz
1/4
i was considerin 4 first ten nos so gafla hua
62a better proof..??
unit''s digit will depend on the unit digit of the previous power multiplied by 3..
so 3, 9, 7, 1, 3, 9 , 7, 1 will be the cyclic way the last digit will behave for given powers.. 1, 2, 3, 4, 5, 6, ...
so the probability of having 9 will be 1/4!
3yep 1/4........... this cylclic behavior is useful in many many sums ive cum across