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How to check if a six sided die is fair?

  • Last Updated : 13 Dec, 2021

Probability is the chance of a wanted result from a pool of all possible results of a probability experiment. A probability experiment can be described as an activity where each attempt yields unplanned results. So, the probability of an experiment is the chance of occurrence of the desired result from all of the possible results of that experiment. The sum of probabilities of the desired and undesired result is always one.

Probability of Desired Result + Probability of Undesired Result = 1

Fair Probability

A probability can be called Fair when there is an equal chance of occurrence of each outcome. No kind of favoritism is observed during the occurrence of any one outcome and each outcome has an equal chance of occurrence. 

For example, Toss of a Coin: Here, each of the possible outcomes of Head and Tail has an equal chance of coming as the outcome. So, the toss of a coin can be considered to qualify for a fair probability.

Unfair Probability

A probability can be called Unfair when there isn’t an equal chance of occurrence of each outcome. Some kind of favoritism is observed during the occurrence of any one outcome and each outcome has an unequal chance of occurrence.

For example, Toss of a Hypothetical Coin having Heads on both its Faces: Here, the possible outcome of the coin is only Head, having a total probability of 1. The probability of having a Tail on the face of the coin is 0. So, the toss of the mentioned hypothetical coin can be considered to qualify for an unfair probability.

How to check if a six sided die is fair?

Answer:

  • Probability when a dice is rolled: 

Total number of possible outcomes  = 6 (1, 2, 3, 4, 5, 6)

  • Probability of having 1 on the roll-up of dice 

= Occurrence of 1 on top of dice/ Total number of possible outcomes of dice

= 1/6

  • Probability of having 2 on the roll-up of dice

= Occurrence of 2 on top of dice/ Total number of possible outcomes of dice

= 1/6

  • Probability of having 3 on the roll-up of dice

= Occurrence of 3 on top of dice/ Total number of possible outcomes of dice

= 1/6

  • Probability of having 4 on the roll-up of dice

= Occurrence of  4 on top of dice/ Total number of possible outcomes of dice

= 1/6

  • Probability of having 5 on the roll-up of dice

= Occurrence of 5 on top of dice/ Total number of possible outcomes of dice

= 1/6

  • Probability of having 6 on the roll-up of dice

= Occurrence of 6 on top of dice/ Total number of possible outcomes of dice

= 1/6

Each of the outcomes of the dice has an equal probability of 1/6. Each outcome is equally likely to come on the top when the dice is rolled. Hence, the rolling of dice can be considered to be a fair probability scenario.

Similar Problems

Question 1: The umpire tosses a coin before the start of the match. Does it qualify as a Fair probability?

Answer: 

When a coin is tossed, there is an equal chance for Heads or Tails to appear. So, it qualifies as a fair probability.

Question 2: Consider a basket with 3 oranges and 3 mangoes. Vaibhav randomly picks one fruit to eat. Will this qualify for a fair probability scenario?

Answer: 

Since Vaibhav randomly picks the fruit and there is no favoritism shown while choosing the fruit. So, yes it qualifies for a fair probability.

Question 3: Does starting the car engine qualify for a fair probability?

Answer: 

Yes, starting the car engine qualifies for a fair probability as there are two cases of either the car starting or not. And both these outcomes have an equal chance of occurrence. So, it qualifies for a fair probability.

Question 4: Outcomes of an event show no kind of favored behavior. Do they qualify for a fair probability scenario?

Answer: 

Yes, since there is no partiality towards any particular outcome. The above scenario qualifies for a fair probability scenario.

Question 5: A fair die is rolled. What will be the probability of obtaining an odd number?

Solution:

The odd numbers present on the die is 1, 3, 5.

Therefore, out of the 6 total occurrences, the possible outcomes are 3.

Probability of obtaining an odd number = 3/6 = 1/2.

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