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he combination lock has three wheels, each numbered from 0 to 9.

a. What is the probability that someone randomly guesses the correct combination in one attempt?

$$
Question 2
Write the probability as a percent.
This is
%.
Question 3
b. You try to guess the combination by writing five different numbers from 0 to 999 on a piece of paper. Explain how to find the probability that the correct combination is written on the paper.
Responses

There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is

, or about 0.5%.
There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is 5 over 999, or about 0.5%.

There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is

, or about 5%.
There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is 5 over 999, or about 5%.

There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is

, or 0.5%.
There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is 5 over 1000, or 0.5%.

There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is

, or 5%.
There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is 5 over 1000, or 5%.

1 answer

To solve the questions regarding the combination lock, let's break it down step-by-step:

Question 1a

The combination lock has three wheels, each numbered from 0 to 9. This means:

  • Each wheel has 10 possible numbers (0 through 9).

  • The total number of combinations can be calculated using the formula:

    \[ \text{Total Combinations} = 10 \times 10 \times 10 = 1000 \]

When guessing randomly, there is only 1 correct combination out of 1000 possible combinations.

Thus, the probability that someone randomly guesses the correct combination in one attempt is:

\[ P(\text{Correct}) = \frac{1}{1000} \]

Question 2

To express this probability as a percentage, we can convert it as follows:

\[ P(\text{Correct}) \text{ as a percentage} = \left(\frac{1}{1000}\right) \times 100% = 0.1% \]

Question 3b

Now you are trying to find the probability of guessing the correct combination if you write down five different numbers from 0 to 999.

As calculated before, there are 1000 possible combinations, not 999. The reason for this is that the combinations range from 000 to 999, which counts all 1000 combinations.

If you have 5 attempts to guess the correct combination, your probability of getting it right can be calculated as follows:

The probability of getting the correct combination is the number of correct combinations you can guess divided by the total number of combinations:

\[ P(\text{Correct}) = \frac{5}{1000} \]

This can also be expressed as a percentage:

\[ P(\text{Correct}) \text{ as a percentage} = \left(\frac{5}{1000}\right) \times 100% = 0.5% \]

Summary of Answers

  • Question 1: The probability of guessing the correct combination in one attempt is \( \frac{1}{1000} \).
  • Question 2: This probability is \( 0.1% \).
  • Question 3: The probability of writing down the correct combination while trying 5 different numbers is \( \frac{5}{1000} \), or \( 0.5% \).