First slide

Theorems of probability

Question

$T h e probability of A = P r o b a b i l i t y o f$ $B= Probability of C= \frac{1}{4}$ , $P(A)∩P(B)∩P(C)=0, P(B∩C)=0$ $and P(A∩C)= \frac{1}{8}, P (A \cap B) = 0$ $the probability that atleast one of the events A, B, C exists is$

Very Easy

Solution

$Probability that at least one of the events A,B,C exists is given by the shaded region.$
$\begin{matrix} Req. prob. = P (A) + P (B) + P (C) - P (A \cap B) - P (B \cap C) - P (C \cap A) + P (A \cap B \cap C) \\ = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} - 0 - 0 - \frac{1}{8} + 0 \\ = \frac{5}{8} \end{matrix}$

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