A and B are two events such that P A -1-4- P - A - B -1-2 and P - B - A -2-3 then P A - B -A- 5-12B- 1-6C- 7-12D- 1-4

The correct option is A P(A)=1/4,P ( B/A )=P(A ∩ B)/P(B)=2/3⇒ P(A ∪ B)=1/6 P ( A/B )=P(A ∩ B)/P(B)=1/2⇒ P(B)=1/3 ∴ P(A ∪ B)=P(A)+P(B) P(A∩ B)=1/4+1/3 1/6=5/1 ...

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Byju's Answer

Standard XII

Mathematics

Characteristics of Axiomatic Approach

A and B are t...

Question

A and B are two events such that P(A) = $\frac{1}{4}$ , P = $(\frac{A}{B})$ = $\frac{1}{2}$ and P = $(\frac{B}{A}) = \frac{2}{3}$ then P $(A \cup B)$ =

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Solution

The correct option is B

$P (A) = \frac{1}{4}, P (\frac{B}{A}) = \frac{P (A \cap B)}{P (B)} = \frac{2}{3} \Rightarrow P (A \cup B) = \frac{1}{6} P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)} = \frac{1}{2} \Rightarrow P (B) = \frac{1}{3} ∴ P (A \cup B) = P (A) + P (B) - P (A \cap B) = \frac{1}{4} + \frac{1}{3} - \frac{1}{6} = \frac{5}{12}$

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Similar questions

If A and B are any two events such that $P (A) = \frac{1}{2}, P (B) = \frac{1}{3}, a n d P (A \cap B) = \frac{1}{4}, t h e n P (A^{'} / B^{'}) =$

Q. If A and B are two events such that

P (A) = \frac{1}{4}, P (B) = \frac{1}{2}

and

P (A \cap B) = \frac{1}{8}

find P

A \cup B

A

and

B

are two events such that

P (A \cup B) = \frac{3}{4}, P (A \cap B) = \frac{1}{4}, P (¯ ¯¯ ¯ A) = \frac{2}{3}

; then

P (¯ ¯¯ ¯ A \cap B)

Q. Two events

A

and

B

are such that

P (A) = \frac{1}{4}, P (A | B) = \frac{1}{4}

and

P (B | A) = \frac{1}{2}

Consider the following statements:
(I)

P (¯ ¯¯ ¯ A | ¯ ¯¯ ¯ B) = \frac{3}{4}

(II)

A

and

B

are mutually exclusive
(III)

P (A | B) + P (A | ¯ ¯¯ ¯ B) = 1

Then

If A and B are two events such that

$P (A) = \frac{1}{2}, P (B) = \frac{1}{3}$ and $P (A \cap B) = \frac{1}{4},$ then find

(iii) $P (\frac{A^{'}}{B}) .$

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A and B are two events such that P(A) = 14 , P = (AB) = 12 and P = (BA)=23 then P (A∪B) =

The correct option is B P(A)=14,P(BA)=P(A∩B)P(B)=23⇒P(A∪B)=16P(AB)=P(A∩B)P(B)=12⇒P(B)=13∴P(A∪B)=P(A)+P(B)−P(A∩B)=14+13−16=512

A and B are two events such that P(A) = $\frac{1}{4}$ , P = $(\frac{A}{B})$ = $\frac{1}{2}$ and P = $(\frac{B}{A}) = \frac{2}{3}$ then P $(A \cup B)$ =