On a door is a little keyboard with the keys 1,2,3,4,5,6,7,8,9,A,B,C,D. The door

Question

On a door is a little keyboard with the keys 1,2,3,4,5,6,7,8,9,A,B,C,D. The door opens when someone types - in order - three numbers and two letters.Each of the numbers in the code are different, but the letters may be the same. We assume in this problem that all the people involved know how the code works, i.e. they know it is made of three different numbers followed by two possibly identical leters so that when they attempt to type the code, they first type 3 numbers and then 2 letters.

a) What is the pobability that someone opens the door in the first try if
i. the persone doesn't know the code?
ii. he/she only remebers hat the 3 numbers in the code are even?
iii. he/she remebers that the 3 numbers are even and the two letters are identical?


b) The door is also equipped with an alarm system that sounds when none of the three numbers typed belong to the code. A child who does not know the code tries to make the alarm sound.

i. What is the probability that he succeeds in his first try?

ii. He tries four times, each of the trials eing independent from each other. What is the probability that the alarm souns at least once during his four trials?

Explanation / Answer

a) i) 9x8x7x4x4 = 8064 1/8064 ii) 4x3x2x4x4 = 384 1/384 iii) 4x3x2x4x1 = 96 1/96 b) i) 1 because if he knows how the code works, he does the letters first it will ring ii) 1 same reasoning

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