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.

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

To create a tree diagram for this experiment, you can start by listing the possible outcomes at each step and connecting them with branches. Here's a visual representation:

Start
/ \
Key1 Key2
/ \ / \
Door 1 Door 2 Door 1 Door 2

In this diagram, "Start" represents the beginning of the experiment, and from there, you have two options: try Key 1 or Key 2. From each of these choices, you have two possible outcomes: either the key opens Door 1 or Door 2.

Now, let's determine the probability of opening the door on the first or second try.

There are five keys in total, and two of them open the door. Therefore, the probability of opening the door on the first try is 2/5. Once you've tried a key and it didn't open the door, there are still four keys left, but only one of them is the correct key. So, the probability of opening the door on the second try is 1/4.

To find the probability of opening the door on the first or second try, you need to add the probabilities of these two events together. Thus, the probability is:

2/5 + 1/4 = 8/20 + 5/20 = 13/20

Therefore, the probability of opening the door on the first or second try is 13/20.