Experimental Probability

Probability means the chances of a number of occurrences of an event. In simple language, it is the possibility that an event will occur or not. The concept of probability can be applied to some experiments like coin tossing, dice throwing, playing cards, etc. Experimental Probability is one of the interesting concepts of Probability. Before diving down into the definition, Let’s start understanding this concept through our daily life situations. We all have heard typical monsoon forecasts like, “Kerala remains under high alert expecting heavy rains and winds as a result of cyclone Burevi” and similar other headlines, right? But have you ever thought that how these expectations sometimes turn into reality? The reason behind the chances, expectations, doubts, forecasts are Probability. Probability in simple meaning gives us the predictions of an event that may or may not be happened based on our past experiences. And these Past experience is based upon the experiment of events. The way of finding the probability through many repeated experiments is known as Experimental Probability.

Experimental Probability vs Theoretical Probability

Experimental Probability

Experimental Probability is found by repeating the experiment and observing outcomes. Experimental Probability for an Event A can be calculated as follows:

P(E) = Number of trials taken in which event A happened / Total number of trials

Now, as we learn the formula, let’s put this formula in our coin-tossing case.  If we tossed a coin for 10 times and recorded a head for 4 times and a tail for 6 times then the Probability of Occurrence of Head on tossing a coin:

P(H) = 4/10

Similarly, Probability of Occurrence of Tails on tossing a coin:

P(T) = 6/10

As we have understood this concept, let’s jump into experiments.

Theoretical Probability

Theoretical Probability deals with assumptions in order to avoid unfeasible or expensive repetition experiments. Theoretical Probability for an Event A can be calculated as follows:

P(A) = Number of outcomes favorable to Event A / Number of all possible outcomes    

Note: Here we assume the outcomes of an event as equally likely.

Now, as we learn the formula, let’s put this formula in our coin-tossing case. In tossing a coin, there are two outcomes: Head or Tail.

Hence, The Probability of occurrence of Head on tossing a coin is

P(H) = 1/2

Similarly, The Probability of occurrence of Tail on tossing a coin is

P(T) = 1/2

Examples of Experimental Probability

Question 1. Let’s take an example of tossing a coin, tossing it 10 times, and recording the observations. By using the formula, we can find the experimental probability for heads and tails as shown in the below table?

Solution:

Number of Times  the coin tossed	Number of times  heads come	Number of times  tails come
1	H	0
2	0	T
3	0	T
4	H	0
5	H	0
6	H	0
7	0	T
8	H	0
9	0	T
10	H	0

The formula for experimental probability:

P(H) =	Number of Heads	6	=	0.6
	Total Number of Trials	10

Similarly,

P(T) =	Number of Tails	4	=	0.4
	Total Number of Trials	10

P(H) + P(T) = 0.6 + 0.4 = 1

Repeat this experiment for ‘n’ times and then you will find that the number of times increases, the fraction of experimental probability comes closer to 0.5. Thus if we add P(H) and P(T), we will get  0.6 + 0.4 = 1 which means P(H) and P(T) is the only possible outcomes.

Question 2. A manufacturer makes 50,000 cell phones every month. After inspecting 1000 phones, the manufacturer found that 30 phones are defective. What is the probability that you will buy a phone that is defective? Predict how many phones will be defective next month?

Solution:

Experimental Probability = 30/1000 = 0.03

0.03 = (3/100) * 100 = 3%

The probability that you will buy a defective phone is 3%

Number of defective phones next month = 3% × 50000

Number of defective phones next month = 0.03 × 50000

Number of defective phones next month = 1500

Question 3. There are about 320 million people living in the USA. Pretend that a survey of 1 million people revealed that 300,000 people think that all cars should be electric. What is the probability that someone chosen randomly does not like the electric car? How many people like electric cars?

Solution:

Now the number of people who do not like electric cars is 1000000 – 300000 = 700000

Experimental Probability =  700000/1000000 = 0.7

0.7 = (7/10) * 100 = 70%

The probability that someone chose randomly does not like the electric car is 70%

The probability that someone like electric cars is  300000/1000000 = 0.3

Let x be the number of people who love electric cars

x = 0.3 × 320 million

x = 96 million

The number of people who love electric cars is 96 million

My Personal Notes arrow_drop_up

Save