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Standard XII

Mathematics

Conditional Probability

If A and B ar...

Question

If A and B are any two events such that P (A) + P (B) − P (A and B) = P (A), then (A) P (B|A) = 1 (B) P (A|B) = 1 (C) P (B|A) = 0 (D) P (A|B) = 0

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Solution

It is given that A and B are events, such that P( A )+P( B )−P( A and B )=P( A ) .

Simplify the above equation.

P( A )+P( B )−P( A and B )=P( A ) P( B )−P( A and B )=0 P( A and B )=P( B ) P( A and B ) P( B ) =1 This is the formula of conditional probability of occurrence of event A after event B.

P( A|B )=1 Thus, out of all the four options, option (B) is correct.

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Similar questions

IF A and B are any two events such that P(A) + P(B) - P (A and B ) = P(A), then
(a) $P (\frac{B}{A}) = 1$
(b) $P (\frac{A}{B}) = 1$
(c) $P (\frac{B}{A}) = 0$
(d) $P (\frac{A}{B}) = 0$

Q. Let

A

and

B

be two events such that

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

. If

0 < P (A) < 1

and

0 < P (B) < 1

, then

P (A \cup B)^{'}

is equal to

Q. If two events A and B are such that P(A) > 0 and

P (B) \neq 1

, then

P (\frac{¯ A}{¯ B})

is equal to

Q. If

A

and

B

are two events such that

A \subset B

and

P (B) \neq 0

, then which of the following is correct?

Q. Let A and B be two events such that

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

. Then,
Statement 1:

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

Statement 2: If

P (A) + P (B) = 1

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