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If a number is selected from 100 to 199. What is the probability that

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If a number is selected from 100 to 199. What is the probability that [#permalink] New post   21 Aug 2023, 22:49
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If a number is selected from 100 to 199. What is the probability that the number will contain either 2 or 3 as at least one of the digits?


A. 34/100

B. 34/99

C. 35/100

D. 35/99

E. 36/100


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Joshuautazi2021
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Re: If a number is selected from 100 to 199. What is the probability that [#permalink] New post   11 Sep 2023, 05:57
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For every group of 10digit, there is one 2. Total of 10group = 10.

For every group of 10 digits, there is one 3, total of 10group = 10.

For number beginning with twenties, there are 10 but to avoid double counting we remove 1 = 9.

For numbers beginning with 3, there are also 9

Numbers that have 2 and 3 are 32 and 23.

P(2) + P(3) - P(2 and 3)

19 + 19 - 2 = 36

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Joshuautazi2021
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Re: If a number is selected from 100 to 199. What is the probability that [#permalink] New post   11 Sep 2023, 05:57
Joshuautazi2021 wrote:
For every group of 10digit, there is one 2. Total of 10group = 10.

For every group of 10 digits, there is one 3, total of 10group = 10.

For number beginning with twenties, there are 10 but to avoid double counting we remove 1 = 9.

For numbers beginning with 3, there are also 9

Numbers that have 2 and 3 are 32 and 23.

P(2) + P(3) - P(2 and 3)

19 + 19 - 2 = 36

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Re: If a number is selected from 100 to 199. What is the probability that [#permalink] New post   11 Sep 2023, 07:44
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Slot method

1*8*8=64

The numbers which contains 2 and 3 as at least one digit = 100 – 64 = 36.

Probability

\(\frac{100}{C^{100}_1}=\frac{36}{100}
\)
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Re: If a number is selected from 100 to 199. What is the probability that [#permalink] New post   15 Sep 2023, 14:37
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20s = one 2 meaning + 10
30s = one 3 meaning + 10
2 or 3 in 10, 40, 50, 60, 70, 80, 90 meaning 8 * 2= 16

20 +16 = 36
36/100 choice e
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Re: If a number is selected from 100 to 199. What is the probability that [#permalink] New post   06 Oct 2024, 00:12
jiayou111 By this logic, we haven't subtracted 132 and 123 (which are AND) digits.

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Re: If a number is selected from 100 to 199. What is the probability that [#permalink]
06 Oct 2024, 00:12
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