Outside a home, there is a 10-key keypad numbered 0 through 9. The correct four-

Question

Outside a home, there is a 10-key keypad numbered 0 through 9. The correct four-digit code will open the garage door. The numbers can be repeated in the code. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code? (a) The number of possible codes is (Type an integer or fraction. Simplify your answer.) (b)The probability that the correct code is given on the first try, assuming that the owner doesn't remember it is (Type an integer or fraction. Simplify your answer.)

Explanation / Answer

(a)

The code has four digits. Digits can be repeated so each digit of code has 10 options. Therefore possibe number of four digits code is 10*10*10*10 = 10000

Answer: 10000

(b)

Out of these 10000 possible codes, only one is correct so the probability that the correct code is given on the first try is

P(first try) = 1/10000 = 0.0001

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