Question

What is the difference between biased and unbiased die $?$

Answer 1

Hint: Basics of a die : A die is basically a cube having single digit numbers ranging from $1\text{ to 6}$ on all it’s faces means there are six faces. There is a specific scheme of numbering on a die i.e. the sum of the numbers on the opposite faces of the die is always equal to $7$ . $\left(1\right)$ The number $1$ will be opposite to number $6$ : $1+6=7$ . $\left(2\right)$ The number $2$ will be opposite to number $5$ : $2+5=7$ . $\left(3\right)$ The number $3$ will be opposite to the number $4$ : $3+4=7$.

Complete step by step answer:
$\left(1\right)$ Unbiased die: All the possible outcomes are equally likely to occur means the probabilities of occurrence of all the outcomes are equal. When a die is rolled, there are a total six possible outcomes which are numbers $1,2,3,4,5,6$ . According to the definition of probability ;
$\Rightarrow \text{Probability = }{\displaystyle \frac{\text{Number of desired outcomes}}{\text{Total number of outcomes}}}$
Here, the probability of each outcome is $P\left(1\right)=P\left(2\right)=P\left(3\right)=P\left(4\right)=P\left(5\right)=P\left(6\right)={\displaystyle \frac{1}{6}}$ , since each and every outcome is equally likely to occur in case of an unbiased die.

$\left(2\right)$ Biased die: A biased die is opposite of an unbiased die i.e. all the outcomes are not equally likely to occur means the probabilities of occurrence of all the outcomes are not equal. Hence, in case of a biased die we will not get correct results.

Note: Equally likely events: These are the events that have the same probability of occurrence. For example: The probability of occurrence of an even number when a dice is rolled is : $P\left(Even\right)={\displaystyle \frac{3}{6}}\text{ or }{\displaystyle \frac{1}{2}}$ ( since there three even numbers possible in the outcome of a die i.e. $2,4,6$ ) . The probability of occurrence of a odd number when a dice is rolled is : $P\left(Odd\right)={\displaystyle \frac{3}{6}}\text{ or }{\displaystyle \frac{1}{2}}$ ( since there three odd numbers possible in the outcome of a die i.e. $1,3,5$ ) . As we can notice that both the probabilities are equal i.e. $P\left(Even\right)=P\left(Odd\right)={\displaystyle \frac{1}{2}}$ , hence both the events are called as equally likely events.