Question

In: Statistics and Probability

What is the probability that seven-digit phone number has one or more repeated digits ? The...

What is the probability that seven-digit phone number has one or more repeated digits ?

The leading number can not be zero (0).

Solutions

Expert Solution

We have to find the probability that the seven-digit phone number has one or more repeated digits.

We can do this also in this way:

P(one or more repeated digits) ~=~ 1 - P(no digits repeated.)

Let us first find for "P(no digits repeated.)"

Let us get favorable ways of feeding the digits at its place without repetition.

9 ways (from 1 to 9) excluding 0 as leading number 9 ways (from 0 to 9) excluding the number previously feed, now 0 will be considered. 8 ways (from 0 to 9) excluding the numbers previously feed. 7 ways (from 0 to 9) excluding the numbers previously feed. 6 ways (from 0 to 9) excluding the numbers previously feed. 5 ways (from 0 to 9) excluding the numbers previously feed. 4 ways (from 0 to 9) excluding the numbers previously feed.

So, favorable ways =

Now, total possible ways =

9 ways (from 1 to 9) excluding 0 as the leading number 10 ways (from 0 to 9) 10 ways (from 0 to 9) 10 ways (from 0 to 9) 10 ways (from 0 to 9) 10 ways (from 0 to 9) 10 ways (from 0 to 9)

thus, total ways =

Thus,

P(one or more repeated digits) ~=~ 1 - P(no digits repeated.)

=========================================================================================

orchestra answered 1 year ago
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