If two events A and B are such that P(A^')=0.3, P(B)= 0.4 and P(A ∩B^')=0.5, then P(B / A ∪B^')

step 1 In this problem we have to find P of B given a union B dash this is P of B intersection A inters

If two events A and B are such that P(A^')=0.3, P(B)= 0.4...

If two events $A$ and $B$ are such that $P\left(A^{\prime}\right)=0.3, P(B)=$ $0.4$ and $P\left(A \cap B^{\prime}\right)=0.5$, then $P\left(B / A \cup B^{\prime}\right)$ equals
(A) $\frac{3}{4}$
(B) $\frac{5}{6}$
(C) $\frac{1}{4}$
(D) $\frac{3}{7}$

Key Concepts

Conditional Probability

Conditional probability quantifies the likelihood of an event occurring given that another event has occurred. It is defined as the probability of the intersection of the two events divided by the probability of the conditioning event, provided that the probability of that conditioning event is greater than zero. This concept is essential in solving problems where the outcome of one event influences the probability of another.

Complement Rule

The complement rule in probability states that the probability of the complement of an event is equal to one minus the probability of the event itself. This rule is useful when it is easier to calculate the probability of an event not happening rather than the event itself.

Union and Intersection of Events

In probability theory, the union of two events represents the occurrence of at least one of the events, while the intersection represents the occurrence of both events simultaneously. Understanding these operations is crucial for combining probabilities, especially when dealing with complex events that can overlap.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is used to calculate the probability of the union of two or more events by considering the probabilities of the individual events and subtracting the probabilities of their intersections. This principle ensures that overlapping probabilities are not double-counted when combining events.

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