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Why is tossing a Coin considered to be a fair way of deciding?

  • Last Updated : 07 Dec, 2021

Probability is the occurrence of the desired set of outcomes from the set of all possible outcomes of an event. In simpler words, the probability is nothing but a general possibility or likeliness of the occurrence of a favorable outcome. The sum of Probabilities of Occurrence of any Favorable plus Unfavorable Outcome is always equal to one. Probability of Favorable Outcome =1 – Probability of Unfavorable Outcome

Some common terms used in probability

Some terms that are not very often heard in mathematics and are heard in probability are given below. These terms are experiments, events, outcomes, favorable events, etc. Let’s learn about their definitions,

  1. Experiment: An experiment is an activity with unknown results.
  2. Event An event refers to different attempts of an experiment with well-defined results 
  3. Outcome: Outcome refers to the final or well-defined results result of different attempts 
  4. Favorable Event Favorable events are the events with the desired outcome/result 

Probability in simple terms is the occurrence of a definite kind of favorable event. It denotes the chances of the occurrence of a particular event out of all the possible outcomes of the event.

Probability of an Event = Chances of Occurrence of Desired Outcome / All Possible Outcomes of an Event

The probability of any desired event is denoted by P(E). The sum of Probabilities of an event can thus be represented by the following formula:

P(E) + P(E’) = 1

Fair Probability Outcome

The probability of occurrence of an event is fair in all aspects when there is an equal chance of occurrence for each of the outcomes and there is no partiality towards any particular outcome. All the possible outcomes have equal chances and there is no kind of favored behavior for any of the outcomes. Losing and Winning have equal chances of occurrence for the desired outcome. 

Example: Consider a bag with 5 red and 5 blue beads and a person randomly selecting any bead at a particular instance of time.

Unfair Probability Outcome

The probability of occurrence of an event is unfair when there is an unequal chance of occurrence for any of the outcomes and there is a partiality towards any particular outcome. In such cases, there is generally some kind of favored behavior for any of the outcomes. Losing and Winning don’t have equal chances of occurrence for the desired outcome. 

Example Consider a dice having numbers 1, 2, 3, 4, 4, 5 on its different faces. Here, the probability of occurrence of each of the outcomes is not likely as 4 occurs twice on the faces of the dice. Thus, it qualifies as an unfair probability.

Why is tossing a Coin considered to be a fair way of deciding?

Answer:

To check if a coin toss is fair, follow the below steps:

  • Possible outcomes when we toss a coin are: two – Heads and Tails

Cha

of Available Heads from Coin Toss = 1

Chances of Available Tails from Coin Toss = 1

  • Probability of Occurrence of Heads 

= Chances of Available Heads from Coin Toss / Total No. of Outcomes of Coin Toss

= 1/2

  • Probability of Occurrence of Tails

= Chances of Available Tails from Coin Toss / Total No. of Outcomes of Coin Toss

= 1/2

Both the outcomes have an equal likely to appear on toss. None of the outcome is favored in any aspect. So, yes toss of a coin qualifies as fair. 

Similar Questions

Question 1: For a fair probability what should be the probability of each individual outcome?

Answer: 

The probability of each outcome should be equally likely for the overall probability of an event to be considered fair.

Ques

2: Is rolling of a die fair?

Answer: 

Yes, each number has a fair probability of occurrence of 1/6.

Question 3: Is switching on of a fan fair?

Answer: 

Yes, each outcome has a fair probability of occurrence of 1/2.

Question 4: Consider a bag with 5 red and 5 blue beads and a person randomly selecting any bead at a particular instance of time. Is this considered fair?

Answer

Yes, each outcome has a fair probability of occurrence. It qualifies as a fair probability.

Question 5: Consider a dice having numbers 1, 2, 3, 4, 4, 5 on its different faces. Is this fair or unfair probability scenario?

Answer: 

Possible outcomes when a die is thrown = 5 different outcomes (1, 2, 3, 4, 5)

  • Chances of Occurrence of 1 on the dice = 1
  • Chances of Occurrence of 2 on the dice = 1
  • Chances of Occurrence of 3 on the dice = 1
  • Chances of Occurrence of 4 on the dice = 2
  • Chances of Occurrence of 5 on the dice = 1
  • Probability of Occurrence of 1 = 1/6
  • Probability of Occurrence of 2 = 1/6
  • Probability of Occurrence of 3 = 1/6
  • Probability of Occurrence of 4 = 2/6
  • Probability of Occurrence of 5 = 1/6

The occurrence of 4 on the dice has a greater probability as compared to other outcomes so, this qualifies as an unfair probability scenario.

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