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# A die has two faces each with number 1,three faces each with number 2 and one face with number 3.If die is rolled once,determine P(not 3)

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

Toolbox:
• 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.