If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and , where denotes the complement of B, then is equal to [2025]

Question

If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and $P (A \cap \bar{B}) = 0.5$ , where $\bar{B}$ denotes the complement of B, then $P (B / (A \cup \bar{B}))$ is equal to [2025]

Smart Achievers · Accepted Answer

(4)

$P (A \cap \bar{B}) = P (A) - P (A \cap B)$

$\Rightarrow P (A \cap B) = P (A) - P (A \cap \bar{B})$

=0.7 – 0.5 = 0.2

Now, $P (A \cup \bar{B}) = P (A) - P (\bar{B}) - P (A \cap \bar{B})$

= 0.7+(1– 0.4) – 0.5 = 0.8

$P (B \cap (A \cup \bar{B})) = P (B \cap A) \cup (B \cap \bar{B})$

$= P (B \cap A) [P (B \cap \bar{B}) = 0]$

= 0.2

Now, $P (B / (A \cup \bar{B})) = \frac{P (B \cap (A \cup \bar{B}))}{P (A \cup \bar{B})} = \frac{0.2}{0.8} = \frac{1}{4}$ .

Solution

Q.
If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and $P (A \cap \bar{B}) = 0.5$ , where $\bar{B}$ denotes the complement of B, then $P (B / (A \cup \bar{B}))$ is equal to [2025]

1 $\frac{1}{3}$

2 $\frac{1}{2}$

3 $\frac{1}{6}$

4 $\frac{1}{4}$

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Solution

Q. If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P(A∩B¯)=0.5, where B¯ denotes the complement of B, then P(B/(A∪B-)) is equal to [2025]

1 13

2 12

3 16

4 14