The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
Given that,
A keypad with 10 buttons marked 0 through 9 is located at the building's entrance.
We have to find how much probability is it that someone will correctly guess an 8-digit entry code.
We know that,
Probability is defined as the ratio of the number of required outcomes to the total number of outcomes.
Based on the details provided;
One outcome is expected if the needed number of outcomes is 8-digits.
Since there are 10 numbers and 8 numbers need to be chosen, the total number of outcomes is ¹⁰C₈.
Considering that the lock can only be opened by 8 digits;
The probability that someone will properly guess a 8-digit input code is
P=1/¹⁰C₈
P=1/10!/8!2!
P=1/10×9/2
P=1/45
P=0.022
Therefore, The probability is it that someone will correctly guess an 8-digit entry code is 0.022.
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