Probability in everyday life, we come across statements such as:
The words ‘most probably’, ‘chances’, ‘doubt’ etc., show the probability of occurrence of an event.
Some Terms Related to Probability
Experiment:
An operation which can produce some welldefined 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.
Trial:
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}.
Event:
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 E_{1} and E_{2} be any two events (not necessarily mutually exclusive events), then P(E_{1} ∪ E_{2}) = P(E_{1}) + P(E_{2})  P(E_{1} ∩ E_{2})Probability of Occurrence of an Event:
The probability of occurrence of an event is defined as:
P(occurrence of an event)
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?
Solution:
Total number of tria1s = 65.
Number of times 4 appeared = 21.
2. A survey of 200families shows the results given below:
No. of girls in the family  2  1  0 


Out of these families, one is chosen at random. What is the probability that the chosen family has 1 girl?
Solution:
Total number of families = 200.
Number of families having 1 girl = 154.
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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