Machine A makes $60%$ of a factory's items, of which $2%$ are defective. Machine B makes the other $40%$ , of which $5%$ are defective. What is the probability that a randomly chosen item is defective?

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For events $A$ and $B$ : $P (A) = 0.5$ , $P (B) = 0.3$ and $P (A \cup B) = 0.65$ . What is $P (A \cap B)$ , and are $A$ and $B$ independent?
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