First slide

Theorems of probability

Question

Suppose E and F are two events of a random experiment. If the probability of occurence of E is $\frac{1}{5}$ and the probability of occurence of F given E is $\frac{1}{10}$ . Then the probability of non-occurance of atleast one of the events E and F is

Moderate

A

$\frac{1}{18}$
B

$\frac{1}{2}$
C

$\frac{49}{50}$
D

$\frac{1}{50}$

Solution

Given that: $P (E) = \frac{1}{5}; P (F / E) = \frac{1}{10}$
                        $P (F \cap E) = P (E) P (\frac{F}{E}) = \frac{1}{50}$
   $P (\bar{F} \cup \bar{E}) = 1 - P (E \cap F)$
                     $= 1 - \frac{1}{50} = \frac{49}{50}$

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