What is the probability that a seven-digit phone number contains the number 7?

Bevan Mcdonald

Bevan Mcdonald

Answered question

2021-01-15

How likely is it that a seven-digit phone number will include the number 7?

Answer & Explanation

sweererlirumeX

sweererlirumeX

Skilled2021-01-16Added 91 answers

We start by locating the complement of the number 7, which is not a phone number with the number 7, since we assume it must appear at least once. The probability of not having a 7 is 9/10 (there are 10 possible digits). Hence,
P(no7)=(910)(910)(910)(910)(910)(910)(910)=(910)7
Hence, the probability that there is at least 1 number 7 is:
P(at least one 7)=1P(no7)
P(at least one 7)=1(910)7
P(at least one 7)0.52252.2%

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