Question

You come home after dark, and porch light is out. You cannot tell which key opens the door.. you randomly try the 5 keys on your ring, 2 keys open your door.

Draw a tree diagram for the experiment &
Find the probability of opening the door on the first or second try.

Answer 1

prob of picking the right key = 2/5

prob of opening on first try = 2/5
prob of opening on 2nd try = (3/5)(2/5) = 6/25
(2nd try has to be Miss, Success)

prob of 1st OR 2nd try
= 2/5 + 6/25 = 16/25