Probability Tree Diagram

Probability Tree Diagram 

A probability Tree Diagram  is simply a way of representing a sequence of events.

Tree diagram particularly illustrates the PROBABILITY since they record all the possible outcomes in a clear and uncomplicated way.

To draw the tree diagram:

• The first event is always represented by a dot.
• From the dot, the branches are drawn to represent all possible outcomes. That is, the outcomes of an event is usually written at the end of the branch
• The probability of each branch is written on the branches.
• We have to repeat the process for the number of events asked.

Example

1. Draw a Tree diagram For tossing a coin

Solution

Step 1:

The first event starts by dot.

           

Step 2:

From the dot, the branches are drawn to represent all possible outcomes.

when we toss a coin, the possible outcomes are heads and tails

let , heads = H

       tails = T

so,

Step 3 

here, we are tossing just a coin for once.

So now we can list out the possible outcomes.

Step 4:

Now, we have to write the outcomes probabilities on the corresponding branches.

That is, Probability of getting heads when toss a coin = 1/2

            Probability of getting tails when toss a coin = 1/2

Hence the above diagram represents the complete Tree Diagram when tossing a coin

Example 2 

1. Draw a Tree diagram For two tosses of a coin

Solution

Step 1:

The first event starts by dot.

Step 2:

From the dot, the branches are drawn to represent all possible outcomes.

when we toss a coin, the possible outcomes are heads and tails

let , heads = H

       tails = T

so,

Step 3:

here we are tossing twice, so again we have to list the possible outcomes for the second toss.

Even when we toss again the same possible outcomes we are going to get that is Heads and Tails.

Step 4 :

Now lets list out all the possible outcomes when we toss a coin twice.

 

Step 4 :

Now, we have to write the outcomes probabilities on the corresponding branches.

That is, Probability of getting heads when toss a coin = 1/2

            Probability of getting tails when toss a coin = 1/2

Step 5 :

Now lets write the probabilities of the final outcomes.

The final outcomes, that is sample space S= { (HH) , (HT) , (TH) , (TT) }

The probability of getting HH = 1/4

The probability of getting HT = 1/4

The probability of getting TH = 1/4

The probability of getting TT = 1/4