Probability class 9___CBSE Based upon the CBSE syllabus

1. Probability
Class 9
Done by : Smrithi Jaya

2. Probability
• Probability
• Probability is the study of the uncertainty.
The uncertainty of any doubtful situation
is measured by means of Probability.
• Uses of Probability
• Probability is used in many fields like
Mathematics, Physical Sciences,
Commerce, Biological Sciences, Medical
Sciences, Weather Forecasting, etc.

3. Basic terms related to
Probability
• Random experiment
• If we are doing an experiment and we don't know
the next outcome of the experiment to occur then
it is called a Random Experiment.
• Trial
• A trial is that action whose result is one or more
outcomes. Example :
• Throw of a dice
• Toss of a coin

4. Probability
• Event
• While doing an experiment, an event will be
the collection of some outcomes of that
experiment.
• Example
• If we are throwing a dice then the possible
outcome for even number will be three i.e. 2,
4, 6. So the event would consist of three
outcomes

5. Probability – An Experimental Approach
• Experimental probability is the result of
probability based on the actual experiments
• the probability depends upon the number of
trials and the number of times the required
event happens.
• If the total number of trials is ‘n’ then the
probability of event D happening is

6. Probability – An Experimental Approach
• Examples
• 1. If a coin is tossed 100 times out of which 49 times we get head and 51
times we get tail.
• a. Find the probability of getting head.
• b. Find the probability of getting tail.
• c. Check whether the sum of the two probabilities is equal to 1 or not.
• Solution
• a. Let the probability of getting head is P(H)
• Let the probability of getting tail is P(T)
• The sum of two probability is
• = P(H) + P(T)

7. • Impossible Events
• While doing a test if an event is not possible to occur then its
probability will be zero. This is known as an Impossible Event.
• Example
• You cannot throw a dice with number seven on it
• Sure or Certain Event
• While doing a test if there is surety of an event to happen then it is said to
be the sure probability. Here the probability is one.
• Example: 1
• It is certain to draw a blue ball from a bag contain a blue ball only.
• This shows that the probability of an event could be
• 0 ≤ P (E) ≤ 1

8. • Example: 2
• There are 5 bags of seeds. If we select fifty seeds at random from each of 5
bags of seeds and sow them for germination. After 20 days, some of the seeds
were germinated from each collection and were recorded as follows:
• What is the probability of germination of
• (i) more than 40 seeds in a bag?
• (ii) 49 seeds in a bag?
• (iii) more than 35 seeds in a bag?
• Solution:
• (i) The number of bags in which more than 40 seeds germinated out of 50 seeds
is 3.
• P (germination of more than 40 seeds in a bag) = 3
5
= 0.6
• (ii) The number of bags in which 49 seeds germinated = 0.
• P (germination of 49 seeds in a bag) =
0
5
= 0
• (iii) The number of bags in which more than 35 seeds germinated = 5.
• So, the required probability =5
5
= 1
Bag 1 2 3 4 5
No. of seeds
germinated 40 48 42 39 41

9. Elementary Event
• Elementary Event
• If there is only one possible outcome of an event to
happen then it is called an Elementary Event.
• Remark
• If we add all the elementary events of an experiment
then their sum will be 1.
• The general form
• P (H) + P (T) = 1
• P (H) + P= 1 (where is ‘not H’).
• P (H) – 1 = P
• P (H) and Pare the complementary events.

10. Example
• What is the probability of not hitting a six in a
cricket match, if a batsman hits a boundary six times
out of 30 balls he played?
• Solution
• Let D be the event of hitting a boundary.
• So the probability of not hitting the boundary will be
𝑃 𝐷 = 𝑁𝑜.𝑜𝑓 𝑡𝑖𝑚𝑒𝑠 𝑏𝑎𝑡𝑠𝑚𝑎𝑛 ℎ𝑖𝑡𝑠 𝑡ℎ𝑒 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦
𝑇𝑜𝑡𝑎𝑙 𝑛𝑜.𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 ℎ𝑒 𝑝𝑙𝑎𝑦𝑒𝑑

11. Thank you
Done by : Smrithi Jaya