# 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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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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Step 1

The author owns a safe combination which consists of four numbers between 0 and 99, and these numbers can be repeated.

There are 100 possible ways for selecting each number in the safe combination. They are, {0, 1, 2,…99}.

Multiplication counting rule:

The multiplication rule is sequence of events in which first event appears in n1 number of ways, second event appears in n2 number of ways and so on till nth event appears in nn number of ways, the total number of outcomes is given by the multiplication rule.

Step 2

Here, the safe combination consists of 4 numbers. Hence, the number of ways each number can be selected is 100. Thus, the total number of possible ways for Safety is,

Step 3

There would be only one correct combination number out of 100,000,000 possible ways.

Let event A denote the correct combination n...

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