An experiment has 10 equally likely outcomes. | vedclass

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(D) Let $n(S) = 10$ be the total number of outcomes. Given $n(A) = 4$,so $P(A) = \frac{4}{10} = \frac{2}{5}$.Let $n(B) = p$,so $P(B) = \frac{p}{10}$.F

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$5$ or $10$

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(D) Let $n(S) = 10$ be the total number of outcomes. Given $n(A) = 4$,so $P(A) = \frac{4}{10} = \frac{2}{5}$.Let $n(B) = p$,so $P(B) = \frac{p}{10}$.For $A$ and $B$ to be independent,$P(A \cap B) = P(A) 	imes P(B) = \frac{2}{5} 	imes \frac{p}{10} = \frac{2p}{50} = \frac{p}{25}$.Since $P(A \cap B) = \frac{n(A \cap B)}{10}$,we have $\frac{n(A \cap B)}{10} = \frac{p}{25}$,which implies $n(A \cap B) = \frac{10p}{25} = \frac{2p}{5}$.Since $n(A \cap B)$ must be an integer,$2p$ must be divisible by $5$. Since $2$ and $5$ are coprime,$p$ must be a multiple of $5$.Given $B$ is non-empty,$p \in \{5, 10\}$.

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is

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