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A coin is tossed thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events `A` and `B` are independent?

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To determine whether the events \( A \) and \( B \) are independent, we will analyze each case provided in the question. Two events \( A \) and \( B \) are independent if the occurrence of one does not affect the occurrence of the other. Mathematically, this can be expressed as: \[ P(A \cap B) = P(A) \cdot P(B) \] ### Step-by-Step Solution: ...
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A coin is tossed twice and the four possible outcomes are assumed to be equally likely. If A is the event, both head and tail have appeared, and B be the event, at most one tail is observed, find P(A),\ P(B),\ P(A//B)\ a n d\ P(B//A)dot

Knowledge Check

  • A coin is tossed n times. The number of all possible events is

    A
    (a) `2^n`
    B
    (b) `2^(2^n)`
    C
    (c) `2^(n^2)`
    D
    (d) `(2^n)^2`
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