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one or more "7"

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one or more "7"

by sanju09 » Tue Mar 17, 2009 3:07 am
What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?

A. 271/900

B. 27/100

C. 7/25

D. 1/9

E. 1/10

OA C
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by scoobydooby » Tue Mar 17, 2009 4:25 am
p(one or more 7)=1-p(no 7)

p(no 7 in any of the 3 digits):

hundreds: can be filled in 8 ways (no 0 and 7)

tens: can be filled in 9 ways (no 7, numbers can be repeated since distinct digits not asked for)

units: can take any 9 values (no 7 +repeats possible)

=8*9*9/900 (900 integers from 100-999)
=18/25

p(one or more than one 7)=1-18/25=7/25 hence C
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