Check whether the probabilities $P (A)$ and $P (B)$ are consistently defined
$P (A) = 0.5, P (B) = 0.4, P (A \cup B) = 0.8$

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Solution

$P (A) = 0.5$

$P (B) = 0.4$

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

$0.8 = 0.5 + 0.4 - P (A \cap B)$

$P (A \cap B) = 0.5 + 0.4 - 0.8$

$= 0.9 - 0.8$

$= 0.1$

Since $P (A \cap B) < P (A)$ & $P (B),$

the given data is consistent

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Similar questions

Check whether the following probabilities P(A) and P(B) are consistently defined
(i) $P (A) = 0.5, P (B) = 0.7, P (A \cap B) = 0.6$
(ii) $P (A) = 0.5, P (B) = 0.4, P (A \cup B) = 0.8$

If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find

(i) P(A ∩ B) (ii) P(A|B) (iii) P(A ∪ B)

Q. If

P (A) = 0.8, P (B) = 0.5

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P (\frac{B}{A}) = 0.4

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P (A \cap B)

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A, B

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P (A) = 0.6, P (B) = 0.4, P (C) = 0.5

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Check whether the probabilities P(A) and P(B) are consistently definedP(A)=0.5,P(B)=0.4,P(A∪B)=0.8

P(A)=0.5P(B)=0.4P(A∪B)=P(A)+P(B)−P(A∩B)0.8=0.5+0.4−P(A∩B)P(A∩B)=0.5+0.4−0.8 =0.9−0.8 =0.1Since P(A∩B)<P(A) & P(B),the given data is consistent

Check whether the probabilities $P (A)$ and $P (B)$ are consistently defined
$P (A) = 0.5, P (B) = 0.4, P (A \cup B) = 0.8$

$P (A) = 0.5$

$P (B) = 0.4$

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

$0.8 = 0.5 + 0.4 - P (A \cap B)$

$P (A \cap B) = 0.5 + 0.4 - 0.8$

$= 0.9 - 0.8$

$= 0.1$

Since $P (A \cap B) < P (A)$ & $P (B),$

the given data is consistent