Math Problem Statement

Express the indicated degree of likelihood as a probability value between 0 and 1.

When using a computer to randomly generate the last digit of a phone number to be called for a​ survey, there is 1 chance in 10 that the last digit is zero.

Solution

To express the degree of likelihood as a probability value between 0 and 1, we use the formula:

Probability=Number of favorable outcomesTotal number of possible outcomes\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

In this case, the favorable outcome is that the last digit is zero (1 chance), and the total number of possible outcomes is 10 (since the last digit can be any digit from 0 to 9).

Thus, the probability is:

P(last digit is 0)=110=0.1P(\text{last digit is 0}) = \frac{1}{10} = 0.1

So, the probability that the last digit is zero is 0.1.

Would you like more details or have any questions about this?


Here are 5 related questions:

  1. What is the probability that the last digit is not zero?
  2. How would the probability change if there were 20 possible outcomes?
  3. Can you convert this probability to a percentage?
  4. What is the complement of this probability?
  5. How would you calculate the probability of randomly generating an odd last digit?

Tip: Probabilities always range between 0 and 1, where 0 means impossible and 1 means certain.

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Math Problem Analysis

Mathematical Concepts

Probability
Ratio

Formulas

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8