If A and B are two events such that P A -1-2- P B -1-3 and P A - B -1-4- then findiii P A - B -

Here, P(A) = 1/2, P(B) = 1/3 and P(A ∩ B) = 1/4 P(A'/B) = 1 P (A/B) = 1 3/4 = 1/4 or P(A'/B) = P(A' ∩ B)/P(B) = P(B) P(A ∩ B)/P(B) = 1/3 1/4/1/3 = 1/12/ ...

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Byju's Answer

Standard XII

Mathematics

Complement of a Set

If A and B ar...

Question

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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Solution

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

$P (\frac{A^{'}}{B}) = 1 - P (\frac{A}{B}) = 1 - \frac{3}{4} = \frac{1}{4} o r P (\frac{A^{'}}{B}) = \frac{P (A^{'} \cap B)}{P (B)} = \frac{P (B) - P (A \cap B)}{P (B)} = \frac{\frac{1}{3} - \frac{1}{4}}{\frac{1}{3}} = \frac{\frac{1}{12}}{\frac{1}{3}} = \frac{1}{4}$

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Similar questions

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

(i) $P (\frac{A}{B}) .$

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

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

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

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

Q. If A and B are events such that

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

P (B) = \frac{1}{3}

and

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

, then find

P (A / B)

Q. A and B are two events such that

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

. Find

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Q. If

A

and

B

are two events such that

P (A \cup B) = \frac{3}{4} . P (A \cap B) = \frac{1}{4}

and

P (¯ ¯¯ ¯ A) = \frac{2}{3}

, then what is

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equal to?

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If A and B are two events such that P(A)=12,P(B)=13 and P(A∩B)=14, then find (iii) P(A′B).

Here, P(A)=12,P(B)=13 and P(A∩B)=14 P(A′B)=1−P(AB)=1−34=14or P(A′B)=P(A′∩B)P(B)=P(B)−P(A∩B)P(B)=13−1413=11213=14

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