Vocabulary
Experimental Probability- one way of estimating the probability of an event.
Event-found by comparing the number of times an event occurs to the total number of trials.
Examples
Let us consider a random experiment.
Let A be an outcome of the random experiment . Then A is called an event.
The Experimental probability of the event A is given by
P(A) = Number of times the event occurs/ Total number of trials
Experimental probability is also known as Relative frequency
definition of Probability.
Lets consider a few examples
Example 1: -
A die is thrown 100 times out of which 5 appears 28 times. Find the experimental probability of getting the number 5?
Solution: -
The Experimental probability of the event A is given by
P(A) = Number of times the event occurs/ Total number of trials
Here die is thrown 100 times. So total number of trails =100
The number 5 occurs 28 times. So the number of times the required event
occurs = 28
Therefore probability of getting the number 5 = 28/100 = 0.28
Example 2: -
A Box contains 15 red balls, 12 blue balls and 13 green
marbles. Find the experimental probability of getting a green ball.
Solution: -
The Experimental probability of the event A is given by
P(A) = Number of times the event occurs/ Total number of trials
Take a ball from the box. Note the color and return the ball.
Repeat a few times (maybe 200 times). Note the number of times a green ball
was picked (Suppose it is 120).
The experimental probability of getting a green ball from
the box is 120/200 = 60/100 = 0.6
Example 3: -
The following are the marks obtained by 1200 students in
a particular examination.
Marks: 100-120 120-140 140-160 160-180 180-200
No of 63 142 500 320 175
Students
Find the probability that a student selected has marks
(i) under 140
(ii) above 180
(iii) between 140 and 200
Solution: -
The Experimental probability of the event A is given by
P(A) = Number of times the event occurs/ Total number of trials
We can see that the total of the marks is 63 + 142 + 500 + 320 + 175 = 1200
(i) We have to find the probability that a selected student get marks under 40.
There are 63 + 142 = 205 students getting marks under 140.
Therefore P(student getting marks under 140)= 205/1200 = 0.17
(ii) We have to find the probability that a selected student get marks above 180.
There are 175 students getting marks above180.
Therefore P(student getting marks above 180) = 175/1200 = 0.15
(iii) We have to find the probability that a selected student get marks between 140 and 200.
There are 500 + 320 + 175 = 995 students getting marks between 140 and 200. Therefore P(student getting marks between 140 and 200) = 995/1200 = 0.83
http://www.probabilityformula.org/experimental-probability-formula.html
Video Help
https://www.youtube.com/watch?v=yK0beFzhtsw
https://www.youtube.com/watch?v=RdehfQJ8i_0
https://www.youtube.com/watch?v=1gV8LXjzE6w
No comments:
Post a Comment