In this blog, we will discuss probability. We know that probability is that part of mathematics that deals with the area of uncertainty. Like on tossing a coin we get head or tail, will India win the toss or not, whether it will rain or not. Learn more about probability class 9.

 

Though probability started with gambling, it has been used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. The probability is a number assigned to an event that tells us the chances of occurring that event.

 

To check the probability we have an experiment. The experiment is a situation involving chance or probability that leads to an outcome. An outcome is a result of a single trial of an experiment. Throwing a coin getting head is an outcome. On throwing dice getting 6 is an outcome. Each outcome or collection of outcomes makes an event.

 

Based on what we directly observe as the outcomes of our trials, we find the experimental or empirical probability. Let n be the total number of trials. The empirical probability P(E) of an event E happening, is given by Probability of E = Number of trials in which the event happened upon The total number of trials.

 

Probability Class 9 - Example 1

 

Sudha, Rahul, Gopal, Rajani, Keshav and Anuj are appearing for an audition test which is being held to select an anchor for annual function. What is the probability of selecting Gopal?

 

Here the total number of students is 6. Number of trials in which the event happened is 1. So Probability of E = 1 by 6.

 

Ok, What is the probability of any of the girls being selected?
Total number of students = 6
Total number of girls = 2
So Probability of girls= number of girls upon total number of students that is 2 by 6.

 

Now, what is the probability of selecting a boy?
Number of boys = 4
Probability of boy = number of boys upon total number students that is4 by6.

 

If the number of boys changes from 4 to 11 and total number of students become 23 then the probability of selecting a boy will be�..
Then Probability of boy = number of boys upon total number students which is 11 by 23.

 

Note that this probability kept changing depending on the number of trials and the number of total events. As in the above example, we observed that the Probability of the boy changes. Earlier it was 4 by 6 later it became 11 by 23. As the number of boys and the number of students changes the probability changes.

 

Probability Class 9 - Example 2

 

A coin is tossed 1000 times with the following frequencies: Head : 455, Tail : 545. Compute the probability for each event.

 

Solution: Since the coin is tossed 1000 times, the total number of trials is 1000. Let us call the events of getting a head and of getting a tail as E and F, respectively. Then, the number of times E happens, i.e., the number of times a head come up, is 455.

 

So, the probability of E = Number of heads upon Total number of trials i.e., Probability of E = 455/1000 = 0.455.

 

Similarly, the probability of the event of getting a tail = Number of tails upon Total number of trials i.e., Probability of F= 545/1000 = 0.545

 

Note that in the example, probability of E + Probability of F = 0.455 + 0.545 = 1, and E and F are the only two possible outcomes of each trial.

 

Probability Class 9 - Example 3

 

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table: Find the probability of getting each outcome.

 

Solution : Let Ei denote the event of getting the outcome i, where i = 1, 2, 3, 4, 5, 6.
Then Probability of the outcome 1 = Probability of E1 =Frequency of 1upon Total number of times the die is thrown = 179/1000 = 0.179
Similarly, Probability of E2 =150/1000=0.15,

 

Probability of E3 =157/1000 = 0.157,
Probability of E4 = 149/1000 = 0.149,
Probability of E5 = 175/1000 = 0.175
Probability of E6= 190/1000 = 0.19
Note that Probability of E1 + Probability of E2 + Probability of E3 + Probability of E4 + Probability of E4 + Probability of E6= 1

 

Also note that:
(i) The probability of each event lies between 0 and 1.
(ii) The sum of all the probabilities is 1.
(iii) E1, E2, . . ., E6 cover all the possible outcomes of a trial.

 

Example: Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardized conditions favourable to germination. After 20 days, the number of seeds that had germinated in each collection was counted and 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 that 35 seeds in a bag?

 

Solution: Total number of bags is 5.
(i) Number of bags in which more than 40 seeds germinated out of50 seeds is 3.
P(germination of more than 40 seeds in a bag) = 5/? = 0.6
(ii) Number of bags in which 49 seeds germinated = 0.
P(germination of 49 seeds in a bag) = 0/5 = 0.
(iii) Number of bags in which more than 35 seeds germinated = 5. So, the required probability =5/
5 = 1.

 

Read More: Surface Area And Volume Of Combination Of Solids With Examples