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If an integer is chosen at random from first 100 positive integers, then the probability that the chosen number is a multiple of 4 or 6 , is
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Verified Answer
The correct answer is:
$\frac{33}{100}$
Let $A$ be the event to be multiple of 4 and $B$ be the event to be multiple of 6
So,$P(A)=\frac{25}{100}, \quad P(B)=\frac{16}{100}$
Thus required probability is
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\Rightarrow P(A \cup B)=\frac{25}{100}$ $+\frac{16}{100}-\frac{8}{100}=\frac{33}{100}$
So,$P(A)=\frac{25}{100}, \quad P(B)=\frac{16}{100}$
Thus required probability is
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\Rightarrow P(A \cup B)=\frac{25}{100}$ $+\frac{16}{100}-\frac{8}{100}=\frac{33}{100}$
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