Question

a passcode on a smartphone consists of 5 digits, and repetition of digits is allowed.
a) determine the number of possible five - digit passcodes.
b) if a person finds a smartphone and randomly enters 5 digits, what is the probability that the correct passcode is entered?
a) the number of possible five - digit passcodes is □.
(type a whole number.)

Explanation:

Step1: Calculate the number of choices for each digit

Each digit in the passcode can be chosen in 10 ways (digits 0 - 9).

Step2: Use the multiplication principle

For a 5 - digit passcode, the total number of possible passcodes is \(10\times10\times10\times10\times10\).

$$10\times10\times10\times10\times10 = 10^{5}=100000$$

Step3: Calculate the probability

The probability \(P\) of entering the correct passcode is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The number of favorable outcomes is 1 (the correct passcode), and the total number of outcomes is \(100000\). So \(P = \frac{1}{100000}\)

Answer:

a) \(100000\)
b) \(\frac{1}{100000}\)