A small combination lock on a suitcase has 5 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 5 digits with no repeats, what is the probability of a person guessing the right combination?
Accepted Solution
A:
Answer: The required probability is 0.3. Step-by-step explanation: Given that a small combination lock on a suitcase has 5 wheels, each labeled with the 10 digits from 0 to 9. An opening combination is a particular sequence of 5 digits with no repeats.We are to find the probability of a person guessing the right combination.If the 5 digits do no repeat, then we have10 options for first digit, 9 options for second digit, 8 options for third digit, 7 options for fourth digit and 6 options for fifth digit. Let A denote the event that the combination is a particular sequence of 5 digits with no repeats.Also, let S be the sample space for the experiment.Then, we have[tex]n(A)=10\times9\times8\times7\times6=30240,\\\\n(S)=10^5=100000.[/tex]Therefore, the probability of even A is given by[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{30240}{100000}=0.3.[/tex]Thus, the required probability is 0.3.