Probablityyy 2

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Let a=33ⁿ where n Îµ N.If exponent n is chosen at random,find the probabality that units digit of a is 9

#Mathematics #Algebra

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8 Answers

1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-02-22 10:51:38

3/10

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24

eureka123 ·2009-02-22 10:56:13

no....[2]

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1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-02-22 10:57:41

y 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
??

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24

eureka123 ·2009-02-22 11:01:58

becoz ans is 1/4...............

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1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-02-22 11:03:06

upar wala post padho

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1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-02-22 11:08:31

yeah 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

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62

Lokesh Verma ·2009-02-22 21:31:04

a 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!

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3

iitimcomin ·2009-02-22 21:33:27

yep 1/4........... this cylclic behavior is useful in many many sums ive cum across

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