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Standard XII

Mathematics

Union of Sets

If A and B ar...

Question

If A and B are two events associated with a random experiment such that $P (A) = 0.3, P (B) = 0.4$ and $P (A \cup B)$ = 0.5, find $P (A \cap B)$

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Solution

We know by addition theorem on probability

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

$\Rightarrow 0.5 = 0.3 + 0.4 - P (A \cap B)$

$P (A \cap B) = 0.3 + 0.4 - 0.5$

= 0.7 - 0.5 = 0.2

$∴ P (A \cap B) = 0.2$

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If A and B are two events associated with a random experiment such that P(A)=0.3,P(B)=0.4 and P(A∪B) = 0.5, find P(A∩B)

We know by addition theorem on probability P(A∩B)=P(A)+P(B)−P(A∩B) ⇒0.5=0.3+0.4−P(A∩B) P(A∩B)=0.3+0.4−0.5 = 0.7 - 0.5 = 0.2 ∴P(A∩B)=0.2

If A and B are two events associated with a random experiment such that $P (A) = 0.3, P (B) = 0.4$ and $P (A \cup B)$ = 0.5, find $P (A \cap B)$

We know by addition theorem on probability

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

$\Rightarrow 0.5 = 0.3 + 0.4 - P (A \cap B)$

$P (A \cap B) = 0.3 + 0.4 - 0.5$

= 0.7 - 0.5 = 0.2

$∴ P (A \cap B) = 0.2$