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A thief steals an ATM card and must randomly guess the correct PIN code that consists of four digits (0 through 9) that must be entered in the correct order. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

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there are 10 options for each slot, 10 x 10 x 10 x 10 = 10000.  1 / 10000 = 0.0001. the answer is 0.001%

The probability of a correct guess on the first try is 0.0001  .

What is probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows

Formula of Probability :

Probability(Event) = [tex]\frac{Favorable Outcomes }{Total Outcomes}[/tex]

According to the question

A thief steals an ATM card and must randomly guess the correct PIN code

Pin code is of 4 digits which include (0 through 9)

Repetition of digits is allowed.

Therefore ,

1 digits can be chosen in 10 ways (0-9 = 10 )

So,

4 digits

10 * 10 * 10 * 10 = 10000

Now, The Probability  of a correct guess on the first try

Using the formula of Probability :

Probability(Event) = [tex]\frac{Favorable Outcomes }{Total Outcomes}[/tex]  

i.e

Probability(Event) = [tex]\frac{1 }{10000}[/tex]

Probability(Event) = 0.0001  

Hence, the probability of a correct guess on the first try is 0.0001  .

To know more about Probability here:

https://brainly.com/question/11234923

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