Evaluate P A - B - if 2 P A - P B -5-13 and P A - B -2-5-

Given, 2P(A) = P (B) = 5/13⇒ P (A) = 5/26 and P (B) = 5/13 Now, P (A/B ) = P(A∩ B)/P(B)⇒2/5 = P(A ∩ B)/5⇒ P(A ∩ B) = 2/5×5/13 = 2/13 Again P (A ∪ B) = P (A ...

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Standard XII

Mathematics

Definition of Relations

Evaluate P A ...

Question

Evaluate $P (A \cup B), i f 2 P (A) = P (B) = \frac{5}{13} a n d P (\frac{A}{B}) = \frac{2}{5} .$

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Solution

Given, $2 P (A) = P (B) = \frac{5}{13} \Rightarrow P (A) = \frac{5}{26} a n d P (B) = \frac{5}{13} N o w, P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)} \Rightarrow \frac{2}{5} = \frac{P (A \cap B)}{5} \Rightarrow P (A \cap B) = \frac{2}{5} \times \frac{5}{13} = \frac{2}{13} A g a i n P (A \cup B) = P (A) + P (B) - P (A \cap B) = \frac{5}{26} + \frac{5}{13} - \frac{2}{13} = \frac{5 + 10 - 4}{26} = \frac{11}{26}$

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Similar questions

Evaluate P (A ∪ B), if 2P (A) = P (B) =and P(A|B) =

Q. Evaluate

P (A \cup B),

2 P (A) = P (B) = \frac{5}{13}

and

P (A | B) = \frac{2}{5}

Q. Evaluate:

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and

P (A | B) = \frac{2}{5} .

Q. Evaluate

P (A \cup B)

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2 P (A) = P (B) = \frac{5}{13}

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P (A \cup B) \times 100

If 2P(A) = P(B) = 5/13 and P(A|B) = 2/5, then P(A U B) = ...

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Evaluate P(A∪B),if 2P(A)=P(B)=513and P(AB)=25.

Given, 2P(A)=P(B)=513⇒P(A)=526andP(B)=513Now,P(AB)=P(A∩B)P(B)⇒25=P(A∩B)5⇒P(A∩B)=25×513=213Again P(A∪B)=P(A)+P(B)−P(A∩B)=526+513−213=5+10−426=1126

Evaluate $P (A \cup B), i f 2 P (A) = P (B) = \frac{5}{13} a n d P (\frac{A}{B}) = \frac{2}{5} .$