Math Problem Statement
Solution
This problem is about finding the probability of selecting 4 digits at random without replacement, in such a way that the digits match the first four digits of your phone number, assuming no repeats in your phone number.
Step-by-step solution:
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Total digits to choose from: The digits are taken from 0-9, so there are 10 possible digits.
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Order matters: Since you're picking 4 digits and writing them in the order picked, the specific arrangement matters. This means we are dealing with permutations, not combinations.
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Probability calculation:
- The first digit of your phone number must match one of the 10 digits you can pick from. So, the chance of picking the correct first digit is .
- After picking the first correct digit, there are only 9 digits left (since we pick without replacement). The chance of picking the correct second digit is .
- For the third digit, there are 8 digits remaining, so the probability of picking the correct third digit is .
- For the fourth digit, there are 7 digits left, so the chance of picking the correct fourth digit is .
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Multiply these probabilities together:
So, the probability of selecting the first four digits of your phone number in order is .
Would you like further details or have any questions?
Related Questions:
- What would the probability be if you were picking 3 digits instead of 4?
- How would the probability change if repetition of digits were allowed?
- What is the probability of selecting any 4 digits in random order without replacement?
- How does the number of possible arrangements of 4 digits change if the total digits available increase to 15?
- How many different ways can you arrange the 4 digits if they are drawn from 10 digits?
Tip: When solving probability questions with permutations, always consider whether the order matters and whether replacement is involved!
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Math Problem Analysis
Mathematical Concepts
Probability
Permutations
Formulas
P = 1/10 * 1/9 * 1/8 * 1/7
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 9-12
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