probability problems trick

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  • Let us go through the Probability Formulas:
    Probability in simple language is defined as ratio of favorable cases to the total number of cases.
    Probability of happening of any event P(A) = fav. number of cases / Total no. of cases = n/N
    If p is the probability of happening of an event A, then  the probability of not happening of that event is P(Ā) = 1- p
    Probability Equations: P (A) ≤ 1, P(A) + P(Ā) = 1.
    Addition theorem: P(X or Y) = P(X) + P(Y) – P (X∩Y)
    or P(X⋃Y) = P(X) + P(Y) – P(X∩Y)
    Mutually exclusive events: Two events are mutually exclusive if they cannot occur simultaneously. For n mutually exclusive events, the probability is the sum of all probabilities of these events:
    p = p1 + p2 + ... + p (n-1) + p (n)
    or
    P (A or B) = P (A) + P (B) where A and B denote mutually exclusive events. 
    Independent events: Two events are independent if the occurrence of one event does not influence the occurrence of other events. Therefore, for n independent events, the probability is the product of all probabilities of independent events:
    p = p1 x p2 x ... x p (n-1) x p (n)
    or P(X and Y) = P(X) x P(Y) , where X and Y denote independent events
    Odds in favor of certain event = No. of successes: No. of failures
    Odds against of an event = No. of failures: No. of successes
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