Outside a home, there is aa 44 -key keypad numbered 11 through 44. The correct sevenseven -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 nothing. (Type an integer or fraction. Simplify your answer.)

Question

Mathematics

Kendall Bennett

9 March, 07:30

Outside a home, there is aa 44 -key keypad numbered 11 through 44. The correct sevenseven -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 nothing. (Type an integer or fraction. Simplify your answer.)

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Sofia · Answer 1

a) The number of possible codes is 16384

b) The probability of entering the code on the firs ttry is 1/16384

Step-by-step explanation:

a) For each of the four digits we have 7 possibilities and the number of one digit doesnt make restrictions on the others, thus, we have to power 4 a total of 7 times. The number of codes available is 4⁷ = 16384

b) There is only 1 code favourable over a total of 16384, as a consequence, the probability of enter the code correctly is 1/16384