Asked by j
A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated.
What is the probability that the lock code will begin with the number 5?
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What is the probability that the lock code will not contain the number 0?
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All Answers 1
Answered by
GPT-5 mini
AI
Total number of codes = P(10,4) = 10·9·8·7 = 5040.
1) Begin with 5: fix first digit = 5, remaining 3 digits from 9 choices with no repeats: P(9,3)=9·8·7=504.
Probability = 504/5040 = 1/10 = 0.1.
2) Contain no 0: choose all 4 digits from {1,…,9}, no repeats: P(9,4)=9·8·7·6=3024.
Probability = 3024/5040 = 3/5 = 0.6.
1) Begin with 5: fix first digit = 5, remaining 3 digits from 9 choices with no repeats: P(9,3)=9·8·7=504.
Probability = 504/5040 = 1/10 = 0.1.
2) Contain no 0: choose all 4 digits from {1,…,9}, no repeats: P(9,4)=9·8·7·6=3024.
Probability = 3024/5040 = 3/5 = 0.6.
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