Social Security Numbers A Social Security number consists of n...

Question

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

Accepted Answer

Welcome back, everyone. A phone number excluding the area code consists of 7 digits in a specific order, and digits may repeat. Suppose you already know the last 3 digits of a person's phone number from a form they filled out. If you randomly get. As the remaining four digits, what is the probability that you correctly guess the entire phone number A says 0.1, B 0.01, C 0.001, and D 0.0001? For this problem, let's understand the context. So we have a seven digit phone number. Let's suppose that we have 7 boxes, 123456, and 7. We already know the last three digits. So we do not need to consider those boxes. And now what we want to do is simply focus on the remaining 4 empty boxes. What we want to understand is that we are arranging digits in a specific order and digits may repeat. So we're going to use the formula and raise the power of K, which is used when we want to fill K slots. With And elements available. Now, what is N? Well, those are the possible digits, right? And the digits that we have range from 0 to 9, meaning the total number is going to be 10, 9 minus 0 + 1. So N is equal to 10. We have 10 possible digits available, and now the number of slots that we are considering or the number of empty slots that we want to fill would be K equals 4. So now, what is the total number of ways to fill 4 empty slots with 10 available elements that would be N to the power of K. And to the power of K. Equals 10 to the power of 4. And now we're looking for the probability of an event A where A represents. Correctly guessing the entire phone number. We want to add a fraction sign, the total number of ways to form a four digit. Sequence is 10 to the power of 4, and that's our denominator. And what about our numerator? Well, there is only one correct sequence, so we're going to introduce 1 into the numerator. So we have 1 divided by 10 to the power of 4, which is 10,000. And now when we divide those, we are going to get 0.0001, which corresponds to the answer choice D. Thank you for watching.

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Key Concepts

Probability

Combinatorics

Random Selection

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