Let $A$ and $B$ be two events such that $P\overline {(A \cup B)} = \frac{1}{6},P(A \cap B) = \frac{1}{4}$ and $P(\bar A) = \frac{1}{4},$ where $\bar A$ stands for complement of event $A$. Then events $A$ and $B$ are

  • [AIEEE 2005]
  • A

    Independent but not equally likely

  • B

    Mutually exclusive and independent

  • C

    Equally likely and mutually exclusive

  • D

    Equally likely but not independent

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Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$,  $ P ( B )=0.7$,  $P ( A \cap B )=0.6$

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Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is.

  • [IIT 2023]

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