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

Question

14. 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) Number of codes = 10^4 = 10000

b) P(in first try) = 1/10000

P = 0.0001

Mathematically, the probability that an event will occur is expressed as a number between 0 and 1. Notationally, the probability of event A is represented by P(A). If P(A) equals zero, event A will almost definitely not occur. If P(A) is close to zero, there is only a small chance that event A will occur.

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