State true or false:When a die is thrown, the probability of getting an odd number less than 3 is 12.

# State true or false:When a die is thrown, the probability of getting an odd number less than 3 is $\frac{1}{2}$.

1. A
True
2. B
False

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### Solution:

Given that a die is thrown once.
We know that the probability is given as the ratio of the number of favorable outcomes with the total number of possible outcomes.
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total possible outcomes n}\left(S\right)}$
Possible outcomes in a single throw of a die are:
$S=\left\{1,2,3,4,5,6\right\}$.
$⇒n\left(S\right)=6$
Let E be the event of getting an odd number less than 3.
There are only numbers which are less than 3 and odd is 1.
$⇒n\left(E\right)=1$
So the required probability is,
$P\left(E\right)=\frac{\mathit{Number of favourable outcomes n}\left(E\right)}{\mathit{Total number of outcomes n}\left(S\right)}$
$⇒P\left(E\right)=\frac{1}{6}$
Thus, the probability of getting a number less than 3 and odd is $\frac{1}{6}$.
Therefore, the given statement is false.
The correct statement would be that the probability of getting a odd number less than 3 is $\frac{1}{6}$.
Hence, option 1 is correct.

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