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In a lottery there are 900 tickets numbered consecutively

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In a lottery there are 900 tickets numbered consecutively [#permalink] New post 05 Jan 2005, 19:01
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In a lottery there are 900 tickets numbered consecutively 100, 101, ..., 998, 999. If a ticket is drawn at random, what is the probability that

(i) the three digits are neither in ascending or descending consecutive order (e.g. not of the form 345 or 765),
(ii) the three digits read the same backwards and forwards?

Please provide your calculation with your answer.
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 [#permalink] New post 05 Jan 2005, 19:50
Quote:
In a lottery there are 900 tickets numbered consecutively 100, 101, ..., 998, 999. If a ticket is drawn at random, what is the probability that

(i) the three digits are neither in ascending or descending consecutive order (e.g. not of the form 345 or 765),
(ii) the three digits read the same backwards and forwards?

Please provide your calculation with your answer.


i) 1-p(the 3 digits are in ascending or descending order)

there are 7 such numbers in ascending order and 7 such numbers in descending vis a vis

123, 234, 345, 456, 567, 678 & 789 (the same set of numbers in reverse order)

p = 1 - 14/900 = 886/900

ii) there are 9 such numbers
111, 222 ..... 999

p = 9/900 = 1/100
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 [#permalink] New post 05 Jan 2005, 20:19
A) 886/900

Nos which are ascending or descending

100s = 1 i.e. 123
200s = 1 i.e. 234
300s = 2 i.e. 345 and 321
400s = 2
500s = 2
600s = 2
700s = 2
800s = 1 only 876
900s = 1 only 987

So P(neither descending or ascending) = 1-14/900 = 886 / 900


B) 1/10

100s = 10 i.e. 101, 111, 121, 131, 141, 151, 161, 171, 181, 191
200s = 10 i.e. 202, 212, 222, 232, 242, 252, 262, 272, 282, 292
300s = 10 i.e. 303, 313 ...
400s = 10
500s = 10
600s = 10
700s = 10
800s = 10
900s = 10

p(e) = 90/900 = 1/10
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PS: Probability - Advanced? [#permalink] New post 06 Jan 2005, 16:10
Not exactly. The official answers are:

(i) 875/900
(ii) 1/9

This does not appear to be too difficult. But, I cannot figure it out. Hence, my subject line.
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 [#permalink] New post 06 Jan 2005, 16:54
(i) 123 234 345 456 567 678 789 & reverse = 210 321 432 543 654 765 876 987 = total 15 cases out of 900.

probablity = 885/900

(ii) 101 202 303 404 505 606 707 808 909
111
121
131
.
.
.10 rows = total 90 cases

spl cases=

probability = 90/900 = 1/10
  [#permalink] 06 Jan 2005, 16:54
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