$\begin{array}{1 1}(A)\;\large\frac{5}{3}\\(B)\;\large\frac{5}{6}\\(C)\;\large\frac{4}{3}\\(D)\;\large\frac{7}{6}\end{array} $

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- Required probability =$\large\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Step 1:

Given A die is rolled

$\therefore$ Total number of outcomes n(S)=6

The die has 2 faces with number 1

The die has 3 faces with number 2

The die has 1 face with number 3

Step 2:

Not 3 means getting faces with number 1 and 2

$\therefore$ There are two faces with number 1 and three faces with number 2

Let E be the event getting a number not 3

$\therefore n(E)=2+3=5$

Step 3:

$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$

$\Rightarrow \large\frac{5}{6}$

Hence (B) is the correct answer.

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