पूर्णांकों 1,2,3, ldots, 50 से एक पूर्णांक या | vedclass

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Question

Given set $=\{1,2,3, \ldots \ldots . .50\}$

$\mathrm{P}(\mathrm{A})=$ Probability that number is multiple of $4$

$P(B)=$ Probability that number

Vedclass · Accepted Answer

$\frac{21}{50}$

Vedclass · Answer

Given set $=\{1,2,3, \ldots \ldots . .50\}$

$\mathrm{P}(\mathrm{A})=$ Probability that number is multiple of $4$

$P(B)=$ Probability that number is multiple of  $6$

$\mathrm{P}(\mathrm{C})=$ Probability that number is multiple of  $7$

Now,

$\mathrm{P}(\mathrm{A})=\frac{12}{50}, \mathrm{P}(\mathrm{B})=\frac{8}{50}, \mathrm{P}(\mathrm{C})=\frac{7}{50}$

again

$ P(A \cap B)=\frac{4}{50}, P(B \cap C)=\frac{1}{50}, P(A \cap C)=\frac{1}{50} $

$ P(A \cap B \cap C)=0$

Thus

$ P(A \cup B \cup C)=\frac{12}{50}+\frac{8}{50}+\frac{7}{50}-\frac{4}{50}-\frac{1}{50}-\frac{1}{50}+0$

$ =\frac{21}{50}$

$P(A)$	$P(B)$	$P(A \cap B)$	$P (A \cup B)$
$\frac {1}{3}$	$\frac {1}{5}$	$\frac {1}{15}$	........

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