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A die is thrown once. What is the probability of getting a number lying between $1$ and $5$ ?

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Answer:

$\dfrac { 1 } { 2 }$

Step by Step Explanation:

1. We know that in a single throw of a die we can get $1, 2, 3, 4, 5,$ or $6.$
   So, the total number of possible outcomes =$6$.
2. Let $E$ be an event of getting a number lying between $1$ and $5$.
   The event $E$ will happen when the number on the die is $2, 3,$ or $4$.
   Thus, the number of favorable outcomes = $3$.
3. We know that the probability of occurrence of an event $E$, denoted by $P(E)$ is defined as $$P(E) = \dfrac { \text { Number of favorable outcomes } } { \text { Total number of possible outcomes } }$$
4. Therefore, $P (\text{ getting a number lying betweeen } 1 \text{ and } 5 ) = P(E) = \dfrac { 3 } { 6 } = \dfrac { 1 } { 2 }$

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