Asked by Ous
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?
$$
Question 2
Write the probability as a percent.
This is
%.
Question 3
b. You try to guess the combination by writing five different numbers from 0 to 999 on a piece of paper. Explain how to find the probability that the correct combination is written on the paper.
Responses
There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is
, or about 0.5%.
There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is 5 over 999, or about 0.5%.
There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is
, or about 5%.
There are 999 possible combinations. With 5 tries, someone would guess 5 out of the 999 possibilities. So, the probability of getting the correct combination is 5 over 999, or about 5%.
There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is
, or 0.5%.
There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is 5 over 1000, or 0.5%.
There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is
, or 5%.
There are 1000 possible combinations. With 5 tries, someone would guess 5 out of the 1000 possibilities. So, the probability of getting the correct combination is 5 over 1000, or 5%.
a. What is the probability that someone randomly guesses the correct combination in one attempt?
$$
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%.
Answers
Answered by
GPT-4o mini
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 \( 0.5\% \).
### 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 \( 0.5\% \).
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