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The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase?
Most Upvoted Answer
The number lock of a suitcase has 4 wheels ,3ach labelled with ten dig...
The number lock has 4 wheels, each labelled with ten digits i.e., from 0 to 9.
Number of ways of selecting 4 different digits out of the 10 digits =
Community Answer
The number lock of a suitcase has 4 wheels ,3ach labelled with ten dig...
Understanding the Lock Mechanism
The suitcase lock consists of 4 wheels, each labeled with the digits from 0 to 9. This means there are a total of 10 unique digits available for selection.
Calculating Total Combinations
Since the lock requires a sequence of 4 digits with no repeats, we can calculate the total number of possible combinations:
- The first wheel can have 10 options (0 to 9).
- The second wheel can have 9 options (one digit is already used).
- The third wheel can have 8 options (two digits are used).
- The fourth wheel can have 7 options (three digits are used).
Total Combinations Calculation:
- Total combinations = 10 * 9 * 8 * 7
Calculating Total Combinations:
- Total combinations = 5040
Probability of Opening the Lock
To find the probability of correctly guessing the right combination on the first attempt, we use the formula:
- Probability = (Number of successful outcomes) / (Total outcomes)
Here, the successful outcome is just 1 (the correct sequence).
Final Probability Calculation:
- Probability = 1 / 5040
Conclusion
Therefore, the probability of a person successfully opening the suitcase lock on their first try is:
- Probability ≈ 0.0001984 or 0.01984%
This illustrates how challenging it is to guess the correct 4-digit sequence without any repeats.
The suitcase lock consists of 4 wheels, each labeled with the digits from 0 to 9. This means there are a total of 10 unique digits available for selection.
Calculating Total Combinations
Since the lock requires a sequence of 4 digits with no repeats, we can calculate the total number of possible combinations:
- The first wheel can have 10 options (0 to 9).
- The second wheel can have 9 options (one digit is already used).
- The third wheel can have 8 options (two digits are used).
- The fourth wheel can have 7 options (three digits are used).
Total Combinations Calculation:
- Total combinations = 10 * 9 * 8 * 7
Calculating Total Combinations:
- Total combinations = 5040
Probability of Opening the Lock
To find the probability of correctly guessing the right combination on the first attempt, we use the formula:
- Probability = (Number of successful outcomes) / (Total outcomes)
Here, the successful outcome is just 1 (the correct sequence).
Final Probability Calculation:
- Probability = 1 / 5040
Conclusion
Therefore, the probability of a person successfully opening the suitcase lock on their first try is:
- Probability ≈ 0.0001984 or 0.01984%
This illustrates how challenging it is to guess the correct 4-digit sequence without any repeats.
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The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase?
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The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase?.
The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number lock of a suitcase has 4 wheels ,3ach labelled with ten digits from 0to 9 .the locks opens with asequence of 4 digits with no repeats .what is the probability ofa a person getting right to open suitcase?.
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