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How to predict a coin flip?

  • Last Updated : 29 Dec, 2021

Probability refers to the chances of a favorable or wished outcome to appear as an outcome out of all the possible outcomes as the result of the probability event. To calculate or predict the probability of any event, all possible scenarios and cases in which different outcomes can appear as result are taken into account. When an event occurs, there is an equal chance of every outcome to be the possible outcome of the event. Wished or desired outcome of a probability event is called a favorable outcome and an undesired outcome is called an unfavorable event. 

The probability of a favorable outcome is denoted by P(E). The probability of an unfavorable outcome is denoted by P(E’). The sum of favorable and unfavorable outcomes of a probability is always one. Given rule always holds true:

P(E) + P(E’) = 1

Prediction of Outcome of a Probability Event

When considering any probability event all possible outcomes are taken into consideration to predict the output. Probability broadly falls into two categories of fair probability and unfair probability. Both are listed as below:

  1. Fair Probability: When there is an equal chance for each outcome to be the result of the probability and there is no favoritism shown towards any particular result. Partiality or favored behavior towards a particular outcome is never observed when we are considering fair probability scenarios. It falls in the category of fair probability. For example: throwing a dice falls in a fair probability case as each of the numbers from 1 to 6 has a probability of 1/6 each. 
  2. Unfair Probability: When there is an unequal chance for each outcome to be the result of the probability and there is some kind of favoritism shown towards any particular result. Partiality or favored behavior towards a particular outcome is observed when we are considering unfair probability scenarios. It falls in the category of unfair probability. For Example: throwing dice with numbers 1, 2, 3, 4, 5, 5. Here the probability of each number is not even, the probability of number 5 is favored. Each of the numbers 1 to 4 have a probability of 1/6 and number 5 has a probability of 2/6.

While predicting results of probability, we consider probability to fall in the fair probability category and each outcome of probability has an equal chance of occurrence. 

Predicting Outcome of a Coin Toss

Predicting results for the probability of the outcome of a coin toss, we consider it a fair probability scenario, and accordingly below steps are followed:

Step 1: Determining possible outcomes

When a fair coin is tossed in air, there are two distinct outcomes expected – Head and Tail. 

Step 2: Checking all the probability rules are followed

There is no favorized behavior towards any of the come, obeying the fair probability rules. Both of the outcomes have experience no partialized treatment while finding the outcome of tossing a coin.

Step 3: Predicting output of the probability event

Probability of occurrence of Head when coin is tossed

= Possible Head in a Coin Flip/ Total Possible Outcomes of a Coin Flip

= 1/2

Probability of occurrence of Tail when coin is tossed

= Possible Tail in a Coin Flip/ Total Possible Outcomes of a Coin Flip

= 1/2

Each of these outcomes has a probability of occurrence of 1/2.

Step 4: Reconfirming the sum of all probability outcomes total to 1

To check if all the possible outcomes are correct we can sum the probabilities of both Head and Tail.

Probability of occurrence of Head when coin is tossed + Probability of occurrence of Tail when coin is tossed

= 1/2 + 1/2

= 1

The sum of probabilities of favorable and unfavorable outcome is always one. Thus, verified that the probability scenario is correct in all aspects.

Similar Questions

Question 1. Predict the output for rolling dice.

Solution:

When we consider the case of rolling of a dice, there are 6 possible outcomes and each has an equal chance of occurrence with a probability with 1/6.

Question 2. Predict the output for picking up the class monitor out of 10 students.

Solution:

When we consider the case of picking up the class monitor, there are 10 possible outcomes and each has an equal chance of becoming monitored with a probability of 1/10.

Question 3. Predict the output for picking up the class monitor will it be a boy or girl, out of given 10 boys and 10 girls.

Solution:

When we consider the case of picking up the class monitor, there are 10 possible outcomes for boys and 10 possible outcomes for girls. Boys and girls have an equal chance of becoming monitored with a probability of 10/20 or 1/2.

Question 4. Predict the output for picking up fruit out of a basket with three mangoes and three apples.

Solution:

The picked fruit to be mango or apple is the same 3/6 or 1/2.

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