Tree Diagram: Overview, Questions, Preparation

Probability 2021 ( Probability )

Rachit Kumar Saxena

Rachit Kumar SaxenaManager-Editorial

Updated on May 12, 2021 09:12 IST

What is a Tree Diagram?

A tree diagram is defined as a visual presentation of a hierarchy in a tree-like diagram in probability theory. A tree diagram is often used to show family relations, classifications, and even so on. However, the tree diagram consists of three features, i.e., node, leaf node, and root node are as follows:

Root Node: A root node is that part that itself a parent node and has no superior parent.
Node: Root Nodes connect the nodes, which both are linked together using line connections, which are known as branches or links. However, it shows the relationship between the members.
Leaf Node: Leaf Nodes are those nodes that do not have any child node and also well-known as end nodes.

Tree_Diagram

Calculation of Overall Probability Using Tree Diagram

Generally, Probability is defined as the likelihood of occurrence of the events. The value of Probability is in numerical form and lies between 0 and 1.

Steps to Calculate Overall Probability

  • Written down the values of Probability on the branches.
  • After that, multiply the value of Probability and the branches.
  • Lastly, make the addition of the obtained probability value after the process of multiplication.

Well, after adding the probability values, your outcome should be 1.

Tree_Diagram_2

Weightage of Tree Diagram

Tree Diagram is a topic of the chapter named Probability. The chapter consumes a total of 8 to 11 marks of weightage in Class X. Each year, you will find 3 or 4 questions in the examination from the chapter Probability. A tree diagram is a part of class 9th, 10th, 11th, or 12th through the chapter of Probability. Apart from the tree diagram, you will get a few other topics in this chapter, such as:

  • Uncertainty
  • Statistical Dispersion
  • Random sequence, and many more.

Illustrated Examples on Tree Diagram

1. An individual has 4 keys, and only 1 key fits the door lock. What is the Probability that the locked door can be unlocked in three tries?

Solution. The Probability (P) of door getting unlocked door in the first attempt = 1/4

The Probability (P) of door getting unlocked door in the second attempt = (3/4)(1/3) = 1/4

The Probability (P) of door getting unlocked door in the third attempt = (3/4)(2/3)(1/2) = 1/4

Tree_Diagram_3

Therefore, the Probability (P) of door getting unlocked door in the three attempts 

= 1/4 + 1/4 + 1/4 = 3/4.

2.A bag consists of 3 black and 5 white pens. Draw the Probability with a tree diagram for two draws.

Solution. Number of Black pens = 3

Number of White pens = 2

Total number of pens = 8

So, the Probability of black balls = 3/8

Probability of white balls = 5/8

Hence, the diagram for two draws of pens with possible outcomes is as follows:

Tree_Diagram_4

 

3.One card is picked from a pack of 52 playing cards, without replacement, and then another one is picked. Calculate the Probability of two red cards using a probability tree.

Solution. The Probability of picking two red cards = 25/102.

FAQs on Tree Diagram

Q: What is a Tree Diagram?

A: A tree diagram is a graphical presentation that shows hierarchical dependencies between individual elements of a network.

Q: Tree Diagram belongs to which chapter?

A: The topic of tree diagrams belongs to the chapter on Probability.

Q: What is the basic formula to find Probability?

A: Probability P (E) of the event = (Number of the favourable outcomes)/(Total number of Outcomes)

Q: What are the applications of Probability in the real era?

A:  Basic knowledge of Probability defines the perception of various other phenomena in our surroundings. Probability is mainly used in sports strategies, weather forecasting, etc.

Q: If P (A) = 7/13, P (B) = 9/13, and P (AΩB), Evaluate P (A/B).

A: P (A/B) = P (AΩB)/ P (B) = (4/13)/(9/13) = 4/9.
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