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Probability Level 3

All phone numbers of a city are made up of exactly 8 digits that don't begin with 0 or 3. What percentage of the numbers begin and end with a 5?


The answer is 1.25.

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Paola Ramírez by Paola Ramírez , 24, Mexico

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1 solution

Discussions for this problem are now closed

Paola Ramírez
Jan 9, 2015

Total number 8 × 10 × 10 × 10 × 10 × 10 × 10 × 10 = 8 × 1 0 7 8 \times 10 \times 10\times 10 \times 10\times 10 \times 10\times10=8\times 10^7

Numbers that begin and end with 5 5 1 × 10 × 10 × 10 × 10 × 10 × 10 × 1 = 1 0 6 1 \times 10 \times 10\times 10 \times 10\times 10 \times 10\times 1=10^6

Percentage

1 0 6 × 100 8 × 1 0 7 = 1.25 \frac{10^6\times 100}{8\times 10^7}=\boxed{1.25}

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Another approach would be to note that the probability that the number begins with a 5 5 is 1 8 \frac{1}{8} , and the probability that it ends with a 5 5 is 1 10 \frac{1}{10} . Thus the desired percentage is 100 ( 1 8 ) ( 1 10 ) = 1.25 100(\frac{1}{8})(\frac{1}{10}) = 1.25 %.

Brian Charlesworth - 6 years, 4 months ago

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