Question

A thief steals an ATM card and must randomly guess the correct three-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try? The number of possible code is__?? (Type an integer or fraction. Simplify your answer) The probability that the correct code is given in the first try is __?? (Type an integer or fraction. Simplify your answer.)

Answer 1

Answer:

1/343

Step-by-step explanation:

Given that:

Required pass code = 3 digit long

Digit or keypad option / length = 7

What is the probability of a correct guess on the first try? To obtain this,

Probability = required outcome / Total possible outcomes

The required outcome = correct guess; which is a single combination of the right digits = 1

Total possible outcomes = number of available combinations or the number of possible codes = (7^3) = 343

Hence,

P(right guess on first try) = required outcome / Total possible outcomes

= 1/343