If P B -3-5- P A - B -1-2 and P A - B -4-5- then find P A - B - P A - B -

Given, nbsp;P(B)=35, P(A|B)=12 and P(A∪ B)=45 Now, P(A|B)=12 ⇒P(A∩ B)P(B)=12 ⇒ P(A∩ B)=12×35=310 P(A∪ B)'+P(A' ∩ B)=1 P(A∪ B)+P(B) P(A∩ B) =1 45+35 310 =12 ...

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Byju's Answer

Standard XII

Mathematics

De Morgan's Law

If P B =3/5, ...

Question

If $P (B) = \frac{3}{5}, P (A | B) = \frac{1}{2}$ and $P (A \cup B) = \frac{4}{5}$ , then find $P (A \cup B)^{'} + P (A^{'} \cap B)$ .

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Solution

Given, $P (B) = \frac{3}{5}, P (A | B) = \frac{1}{2}$ and $P (A \cup B) = \frac{4}{5}$
Now, $P (A | B) = \frac{1}{2}$
$\Rightarrow \frac{P (A \cap B)}{P (B)} = \frac{1}{2}$
$\Rightarrow P (A \cap B) = \frac{1}{2} \times \frac{3}{5} = \frac{3}{10}$

$P (A \cup B)^{'} + P (A^{'} \cap B) = 1 - P (A \cup B) + P (B) - P (A \cap B)$
$= 1 - \frac{4}{5} + \frac{3}{5} - \frac{3}{10}$
$= \frac{1}{2}$

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If P(B)=35, P(A|B)=12 and P(A∪B)=45, then find P(A∪B)′+P(A′∩B).

Given, P(B)=35, P(A|B)=12 and P(A∪B)=45 Now, P(A|B)=12 ⇒P(A∩B)P(B)=12 ⇒P(A∩B)=12×35=310 P(A∪B)′+P(A′∩B)=1−P(A∪B)+P(B)−P(A∩B) =1−45+35−310 =12

If $P (B) = \frac{3}{5}, P (A | B) = \frac{1}{2}$ and $P (A \cup B) = \frac{4}{5}$ , then find $P (A \cup B)^{'} + P (A^{'} \cap B)$ .