$A$ batch of pencils contains $12$ good,$6$ slightly defective,and $2$ very defective pencils. If a pencil is selected at random,what is the probability that it is a non-defective pencil?

  • A
    $3/5$
  • B
    $3/10$
  • C
    $4/5$
  • D
    $1/2$

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If $A$ and $B$ are any two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,then the events $A$ and $B$ are

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