Probability as Relative Frequency

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In multiple choice questions, normally there are five options and the one correct answer. If a student choose an option at random, there is 1/5 probability (20% chances) of selecting the right answer.

It also means that if a student do not know anything about the subject, he will choose the one right answer out of five questions. And, if there are 20 questions in total he will (on average) choose the 4 answers correctly.

Probability is True on Average
It does not mean the student exactly choose the 4 correct answers out of 20 multiple choice questions. It means, the student will choose around 4 correct answers. It also could be 3 or 5. But, it will remain close to 4.

So, the formula for Probability of Relative Frequency is


Where n is the number of trials, and r(n) is the number of events in which we are interested in.

As we know that the probability of appearing 6 in rolling a dice is 1/6 (0.16). Similarly, it does not mean the 6 will appear one time in six rolls, it means around one time. It also could be 0 or 2. And, in 12 rolls six will shown around 2 times (it also could be 1 or 3 times) and around 3 times in 18 rolls, and so on….

We roll the dice different times and calculate the numbers of times the number 6 is shown.

Dice Rolled: 10 times, No: of sixes: 2, Probability: 2/10 (0.2)
Dice Rolled: 20 times, No: of sixes: 3, Probability: 3/20 (0.15)
Dice Rolled: 30 times, No: of sixes: 7, Probability: 7/30 (0.23)
Dice Rolled: 40 times, No: of sixes: 4, Probability: 4/40 (0.1)
Dice Rolled: 50 times, No: of sixes: 8, Probability: 8/50 (0.16)
Dice Rolled: 60 times, No: of sixes: 8, Probability: 8/60 (0.133)
Dice Rolled: 70 times, No: of sixes: 10, Probability: 10/70 (0.143)
Dice Rolled: 80 times, No: of sixes: 12, Probability: 12/80 (0.15)
Dice Rolled: 90 times, No: of sixes: 14, Probability: 14/90 (0.155)
Dice Rolled: 100 times, No: of sixes: 16, Probability: 16/100 (0.16)

So, as we are increasing the number of trials (n) we are going towards the probability of appearing 6, that is 1/6.