Question

(35) Cards are numbered 101 to 200 A card is drawn. Find the probability
of getting (a) a perfect square (b) number divisible by 7​

Answer 1

$\LARGE\textsf{\underline\textcolor{aqua}{↭ SoLuTioN :-}}$

$\large\textsf{ }$

↦ Let S be the Sample Space of cards numbered from 101 to 200 .

∴ n ( S ) = 101

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$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\underline{\large\textsf{Even A :- Getting a perfect square}}$

$\large\textsf{ }$

∴ A = { 121 , 144 , 169 , 196 }

∴ n ( A ) = 4

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{ P ( A )= \cfrac{\large\textsf{n ( A )}}{\large\textsf{n ( S )}} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ = \cfrac{\large\textsf{4}}{\large\textsf{101}} }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{ ∴ P ( A ) = \cfrac{\large\textsf{4}}{\large\textsf{101}} }}$

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$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\underline{\large\textsf{Even B :- Number divisible by 7}}$

$\large\textsf{ }$

$\large\textsf{ }$∴ B = { 105 , 112 , 119 , 126 , 133 , 140 , 147 , 154 , 161 , 168 , 175 , 182 , 189 , 196 }

∴ n ( B ) = 14

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{P ( B ) = \cfrac{\large\textsf{n ( B )}}{\large\textsf{n ( S )}} }$

$\qquad\tt{:}\longrightarrow\large\textsf{ = \cfrac{\large\textsf{14}}{\large\textsf{101}} }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{ ∴ P ( B )= \cfrac{\large\textsf{14}}{\large\textsf{101}} }}$

$\large\textsf{ }$

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