State true or false:A die is thrown once. The probability of getting: a number lying between 2 and 6 is 12.

# State true or false:A die is thrown once. The probability of getting: a number lying between 2 and 6 is $\frac{1}{2}$.

1. A
True
2. B
False

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### Solution:

Given that a die is rolled once.
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
As a die is rolled once.
The total possible outcome, $n\left(S\right)=6$
Let E be the event of getting a number lying between 2 and 6. Then,
$E=\left\{3,4,5\right\}$
$⇒n\left(E\right)=3$
The probability of the event E is,
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total number of outcomes n}\left(S\right)}$
$⇒P\left(E\right)=\frac{3}{6}$
$⇒P\left(E\right)=\frac{1}{2}$ Thus, the probability a number lying between 2 and 6 is $\frac{1}{2}$.
Therefore, the given statement is true.
Hence, option 1 is correct.

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