Math CentralQuandaries & Queries


Question from star:

What do you think the probability of finding the last 3 digits of a telephone number if the 1st digit begins with 7?

Hi Star,

The best way to describe probability is total possible outcomes for the situation divided by the total possible outcomes. For example the probability of drawing an ace from a deck of cards would be 4/52 (or 1/13) since there are 4 aces and a total of 52 cards. The fundamental counting principle allows us to determine the total number of options by multiplying them together. For example, say you have 4 shirts, 3 pairs of pants and 2 pairs of shoes that all match each other. The total number of outfits would be 4*3*2=24.

In your situation we first need to figure out the total number of phone numbers that begin with 7. There are 7 digits total, the first digit is known while the others can be 0-9 (10 numbers). How many possible phone numbers are there with the first digit a 7? If the situation you seek is that you know the last three digits in order then you know the first digit and the last three digits so the three remaining digits can be 0 to 9. This is 10 × 10 × 10 possibilities.

Janice and Harley

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