Subjective Type

A die is thrown find the probability of following events: (i) A prime number will appear (ii) A number greater than or equal to $$3$$ will appear (iii) A number less than or equal to one will appear (iv) A number more than $$6$$ will appear (v) A number less than $$6$$ will appear

Solution

The sample space of the given experiment is given by,
$$S = \{1, 2, 3, 4, 5, 6\}$$
(i) Let $$A$$ be the event of the occurrence of a prime number $$\Rightarrow A = \{2, 3, 5\}$$
$$\displaystyle

\therefore P\left ( A \right

)=\frac{Number\,of\,outcomes\,favourable\,to\,A}{Total\,number\,of\,possible\,outcomes\,}=\frac{n\left

( A \right )}{n\left ( S \right )}=\frac{3}{6}=\frac{1}{2}$$
(ii) Let $$B$$ be the event of the occurrence of a number greater than or equal to $$3$$ $$\Rightarrow B = \{3, 4, 5, 6\}$$
$$\displaystyle

\therefore P\left ( B \right

)=\frac{Number\,of\,outcomes\,favourable\,to\,B}{Total\,number\,of\,possible\,outcomes\,}=\frac{n\left

( B \right )}{n\left ( S \right )}=\frac{4}{6}=\frac{2}{3}$$
(iii) Let $$C$$ be the event of the occurrence of a number less than or equal to one $$\Rightarrow C = \{1\}$$
$$\displaystyle

\therefore P\left ( C \right

)=\frac{Number\,of\,outcomes\,favourable\,to\,C}{Total\,number\,of\,possible\,outcomes}=\frac{n\left

( C \right )}{n\left ( S \right )}=\frac{1}{6}$$
(iv) Let $$D$$ be the event of the occurrence of a number greater than $$6$$ $$\Rightarrow D=\phi $$
$$\displaystyle

\therefore P\left ( D \right

)=\frac{Number\,of\,outcomes\,favourable\,to\,D}{Total\,number\,of\,possible\,outcomes}=\frac{n\left

( D \right )}{n\left ( S \right )}=\frac{0}{6}=0$$
(v) Let $$E$$ be the event of the occurrence of a number less than $$6$$ $$\Rightarrow E = \{1, 2, 3, 4, 5\}$$
$$\displaystyle

\therefore P\left ( E \right

)=\frac{Number\,of\,outcomes\,favourable\,to\,E}{Total\,number\,of\,possible\,outcomes}=\frac{n\left

( E \right )}{n\left ( S \right )}=\frac{5}{6}$$

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