- What is Probability
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- Why we need Probability and what is the use of it
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- few terms related to Probability
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- Zeros or roots of the probability
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- Empirical Probability
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- Some Important points about Probability
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- Solved Examples

It is widely used in the study of Mathematics, Statistics, Gambling, Physical sciences, Biological sciences, Weather forecasting, Finance etc. to draw conclusions. Insurance companies uses this to decide on financial policies

1. when we coin is tossed,the possible outcome are Head and Tail.So sample space

$S={H,T}$

2. When a dice is thrown , the possible outcome is 1,2,3,4,5,6. So Sample space

$S={1,2,3,4,5,6}$

$S={H,T}$

2. When a dice is thrown , the possible outcome is 1,2,3,4,5,6. So Sample space

$S={1,2,3,4,5,6}$

- Experimental or empirical probability is an estimate that an event will happen based on how often the event occurs after performing an experiment in a large number of trials.
- It is a probability of event which is calculated based on experiments

- Empirical probability depends on experiment and different will get different values based on the experiment
- If the event A, B, C covers the entire possible outcome in the experiment. Then,

$P (A) +P (B) +P(C) =1$ - The probability of an event (U) which is impossible to occur is 0. Such an event is called an impossible event

P (U)=0 - The probability of an event (X) which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event

$P(X) =1$ - Probability of any event can be as

$0 \geq P(E) \geq 1 $

A coin is tossed 1000 times; we get 499 times head and 501 times tail

a. What is the empirical probability of getting head ?

b. What is the empirical probability of getting tail?

c. Does the sum of above two probability equals 1?

a. $Empirical \; probability \; of \; getting \; head=\frac {(No \; of \; trails \; which \; heads \; came)}{(Total \; Number \; of \; trials)}$

Empirical probability of getting head=499/1000

So empirical or experimental probability of getting head P(H) is calculated as

=.499

b. $Empirical \; probability \; of \; getting \; Tail=\frac {(No \; of \; trails \; which \; tail \; came)}{(Total \; Number \; of \; trials)}$

Empirical probability of getting head=501/1000

So empirical or experimental probability of getting head P(T) is calculated as

=.501

c. Now P(H) +P(T)= .499+.501=1

As tail and head are the only possible outcome,the sum of probabilities is 1

The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times.

(i) What is the probability that on a given day it was correct?

(ii) What is the probability that it was not correct on a given day?

i. Probability that on a given day it was correct = No of day it was correct/Total number of days

=127/250=.7

ii. Number of days it was incorrect=250-175=75

probability that it was not correct on a given day=No of day it was incorrect/Total number of days

=75/250=.3

100 seeds were selected at random from each of 5 bags of seeds, and were kept under standardised conditions favourable to germination. After 20 days, the number of seeds which had germinated in each collection were counted and recorded as follows:

What is the probability of germination of

(i) more than 60 seeds in a bag?

(ii) 51 seeds in a bag?

(iii) more that 75 seeds in a bag?

(iv) 90 seeds in a bag?

Total number of bags is 5.

(i) Number of bags in which more than 60 seeds germinated out of 50 seeds is 4.

P(germination of more than 60 seeds in a bag) = 4/5

(ii) P(51 seeds in a bag) =1/5

(iii) P(more that 75 seeds in a bag) =1/5

(iv) P(90 seeds in a bag) =0/5 =0

1. probability based on outcome of trials

5. Another six letter word of Probability

6. probability of sure event

2. The numerical measure of prediction

3. ______is an action which results in one or several outcomes

4. Probability of impossible event

7. _____ for an experiment is the collection of some outcomes of the experiment.

Check your Answer

Class 9 Maths Class 9 Science