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If A and B are any two events such that P(A)+P(B)-P(A and B)=P(A), then
A. P(B \mid A)=1
B. \mathrm{P}(\mathrm{A} \mid \mathrm{B})=1
C. P(B \mid A)=0
D. P(A \mid B)=0
CBSE | Class 12 | Maths | NCERT | Probability
If A and B are any two events such that P(A)+P(B)-P(A and B)=P(A), then
A. P(B \mid A)=1
B. \mathrm{P}(\mathrm{A} \mid \mathrm{B})=1
C. P(B \mid A)=0
D. P(A \mid B)=0

Solution:

Answer: B. P(A \mid B)=1

Explanation:

The following information is provided in the question:

A and B are two examples of situations in which,
Thus evaluating we have,
P(A)+P(B)-P(A and B)=P(A)

P(A)+P(B)-P(A \cap B)=P(A)

P(B)-P(A \cap B)=0

P(A \cap B)=P(B)

\therefore P(A \mid B)=\frac{P(A \cap B)}{P(B)}

=1

Hence, option B is correct

 

 

 

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