In Exercises 5–36, express all probabilities as fractions. Safety with Numbers  The author owns a safe in which he stores all of his great ideas for the next edition of this book. The safe “combination” consists of four numbers between 0 and 99, and the safe is designed so that numbers can be repeated. If another author breaks in and tries to steal these ideas, what is the probability that he or she will get the correct combination on the first attempt? Assume that the numbers are randomly selected. Given the number of possibilities, does it seem feasible to try opening the safe by making random guesses for the combination?

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Asked Dec 29, 2019
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In Exercises 5–36, express all probabilities as fractions. 

Safety with Numbers  The author owns a safe in which he stores all of his great ideas for the next edition of this book. The safe “combination” consists of four numbers between 0 and 99, and the safe is designed so that numbers can be repeated. If another author breaks in and tries to steal these ideas, what is the probability that he or she will get the correct combination on the first attempt? Assume that the numbers are randomly selected. Given the number of possibilities, does it seem feasible to try opening the safe by making random guesses for the combination?

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Expert Answer

Step 1

The probability that he or she will get the correct combination on the first attempt is 0.000000255 and it is calculated below:

 

From the given information, the combination consists of 4 numbers between 0 and 99. That is, the total numbers are 100 and the possible numbers for the combinations is,

Statistics homework question answer, step 1, image 1
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Step 2

There are only one of 3921225 possibilities ...

Statistics homework question answer, step 2, image 1
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