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(B) Let the two events be $A$ and $B$. Given,$P(A) = \frac{2}{5}$ and $P(B') = \frac{3}{10}$.Since $A$ and $B$ are independent events,their complement

Vedclass · Accepted Answer

$\frac{27}{50}$

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(B) Let the two events be $A$ and $B$. Given,$P(A) = \frac{2}{5}$ and $P(B') = \frac{3}{10}$.Since $A$ and $B$ are independent events,their complements $A'$ and $B$ are also independent.We find the probability of occurrence of $B$ as $P(B) = 1 - P(B') = 1 - \frac{3}{10} = \frac{7}{10}$.We find the probability of non-occurrence of $A$ as $P(A') = 1 - P(A) = 1 - \frac{2}{5} = \frac{3}{5}$.The probability that only one of the two events occurs is given by $P(A \cap B') + P(A' \cap B)$.Since the events are independent,this is $P(A)P(B') + P(A')P(B)$.Substituting the values: $\frac{2}{5} 	imes \frac{3}{10} + \frac{3}{5} 	imes \frac{7}{10} = \frac{6}{50} + \frac{21}{50} = \frac{27}{50}$.

The probability of occurrence of an event is $\frac{2}{5}$ and the probability of non-occurrence of another event is $\frac{3}{10}$. If these events are independent,then the probability that only one of the two events occur is

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