Question

iv) If n(A) = 4, n(s) = 12, then find P(A)
​

Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

• $\large\textsf{n( A ) = 4}$
• $\large\textsf{n ( S ) = 12}$

$\LARGE\textbf{\underline{\underline{To find :-}}}$

• $\large\textsf{P ( A ) = ?}$

$\LARGE\textbf{\underline{\underline{Formula :-}}}$

• $\large\boxed{\textbf{P ( A ) = \cfrac{n( A ) }{n( S )} }}$

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

$\large\leadsto\textsf{P ( A ) = \cfrac{n( A ) }{n( S )} }$

$\large\leadsto\textsf{P ( A ) = \cfrac{4}{12} }$

• $\large\boxed{\textbf{P ( A ) = \cfrac{1}{3} }}$

$\LARGE\textbf{\underline{\underline{Here :-}}}$

• n ( A ) = Total no. of outcomes of event A.

• n ( S ) = Total no. of sample spaces

• P ( A ) = Probability of event A

______________________________

• What are sample spaces :-

↪️ The set of possible outcomes of a random experiment is called the sample spaces . It is denoted by ' S ' or ' Ω ' . Each element of sample spaces is called a ' sample point ' .

______________________________

• What is an event :-

↪ ️The outcomes satisfying particular condition are called favourable outcomes. A set of favourable outcomes of a given sample space is an event .

______________________________

• For more information :-

• Types of events :-

1. Certain event \ Sure event.
2. Impossible event.
3. Simple \ Elementary event.
4. Complement of an event.
5. Mutually exclusive events.
6. Exhaustive event.

Answer 2

$\huge \sf{ \blue{\underline{\underline{Given : }}}}$

• ${\orange{\large\textsf{n( A ) = 4}}}$
• ${\orange{\large\textsf{n ( S ) = 12}}}$

$\huge\sf{ \pink{\underline{\underline{To \: find :}}}}$

• ${ \purple{\large\textsf{P ( A ) = ?}}}$

$\huge\sf{ \green{\underline{\underline{Solution :}}}}$

$\large\implies\textsf{P ( A ) = \cfrac{n( A ) }{n( S )} } \\ \\ \large\implies\textsf{P ( A ) = \cfrac{4}{12} } \\ \\ \large \implies\boxed{\textsf{ \red{P ( A ) = \cfrac{1}{3} }}}$