Probability in everyday life, we come across statements such as:

  1. Most probably it will rain today.
  2. Chances are high that the prices of petrol will go up.
  3. I doubt that he will win the race.

The words ‘most probably’, ‘chances’, ‘doubt’ etc., show the probability of occurrence of an event.

Some Terms Related to Probability


An operation which can produce some well-defined outcomes is called an experiment. Each outcome is called an event. 

Random Experiment:

In an experiment where all possible outcomes are known and in advance if the exact outcome cannot be predicted, is called a random experiment.

Thus, when we throw a coin we know that all possible outcomes are Head and Tail.
But, if we throw a coin at random, we cannot predict in advance whether its upper face will show a head or a tail.

So, tossing a coin is a random experiment.
Similarly, throwing a dice is a random experiment.

To know more about random experiments in details Click Here.


By a trial, we mean performing a random experiment.

For example; throwing a die or tossing a coin etc.

Sample space:

A sample space of an experiment is the set of all possible results of that random experiment.

For example; in throwing a die possible results are {1, 2, 3, 4, 5, 6}.


Out of the total results obtained from a certain experiment, the set of those results which are in favor of a definite result is called the event and it is denoted as E.

Equally Likely Events:

When there is no reason to expect the happening of one event in preference to the other, then the events are known equally likely events.

For example; when an unbiased coin is tossed the chances of getting a head or a tail are the same.

Exhaustive Events:

All the possible outcomes of the experiments are known as exhaustive events.

For example; in throwing a die there are 6 exhaustive events in a trial.

Favorable Events:

The outcomes which make necessary the happening of an event in a trial are called favorable events.

For example; if two dice are thrown, the number of favorable events of getting a sum 5 is four,

i.e., (1, 4), (2, 3), (3, 2) and (4, 1).

Additive Law of Probability:

If E1 and E2 be any two events (not necessarily mutually exclusive events), then P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

Probability of Occurrence of an Event:

The probability of occurrence of an event is defined as:

P(occurrence of an event)

                    Number of trials in which event occurred
                  =                       Total number of trials              

Solved examples on Probability:

1. A dice is thrown 65 times and 4 appeared 2 1 times. Now, in a random throw of a dice, what is the probability of getting a 4?


Total number of tria1s = 65.

Number of times 4 appeared = 21.

Probability of getting a 4 = Number of times 4 appeared/Total number of trials

                                  = 21/65

2. A survey of 200families shows the results given below:

    No. of girls in the family        2         1         0    
No. of Families

Out of these families, one is chosen at random. What is the probability that the chosen family has 1 girl?


Total number of families = 200.

Number of families having 1 girl = 154.

Probability of getting a family having 1 girl

                               = Number of families having 1 girl/Total number of families

                               = 154/200

                               = 77/100

Worksheet Probability:

1. The tree diagram above represents three events. In the first event either a Red, White, or Blue circle is chosen. In the second event either a Red, White, or Blue circle is chosen. In the third event either a Red, White, or Blue circle is chosen.

Match the following events with the corresponding probabilities:

(a) The second circle is white (a) 10/15

(b) All three circles are red (b) 4/15

(c) Exactly two circles are the same (c) 5/15

(d) At least two circles are the same (d) 3/15

(e) The first circle is not red (e) 1/15

(f) The first two circles are blue (f) 12/15

(g) The third circle is blue (g) 15/15

2. The tree diagram above represents three events. In the first event either an A, B, or C is chosen. In the second event either an A, B, or C is chosen. In the third event either a D, E, or F is chosen.

Match the outcome with its probability:

(a) The second letter is a C (a) 6/12

(b) The first or second letter is an A (b) 0/12

(c) The last letter chosen is a D (c) 5/15

(d) The first two letters chosen are both A (d) 3/15

(e) All three letters are the same (e) 1/15

(f) The first letter is not an A (f) 12/15

(g) ADD (g) 15/15


8th Grade Math Practice

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