If P(A) = frac{2}{3},P(B) = frac{4}{9} and P( | vedclass

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(A) The formula for the union of two events is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Given values are $P(A) = \frac{2}{3}$,$P(B) = \frac

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$\frac{4}{5}$

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(A) The formula for the union of two events is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Given values are $P(A) = \frac{2}{3}$,$P(B) = \frac{4}{9}$,and $P(A \cap B) = \frac{14}{45}$.Substituting these values into the formula:$P(A \cup B) = \frac{2}{3} + \frac{4}{9} - \frac{14}{45}$.To add and subtract these fractions,find the least common multiple $(LCM)$ of the denominators $3, 9, 45$,which is $45$.$P(A \cup B) = \frac{2 	imes 15}{45} + \frac{4 	imes 5}{45} - \frac{14}{45}$.$P(A \cup B) = \frac{30}{45} + \frac{20}{45} - \frac{14}{45}$.$P(A \cup B) = \frac{30 + 20 - 14}{45} = \frac{36}{45}$.Simplifying the fraction by dividing both numerator and denominator by $9$,we get:$P(A \cup B) = \frac{4}{5}$.

If $P(A) = \frac{2}{3}$,$P(B) = \frac{4}{9}$ and $P(A \cap B) = \frac{14}{45}$,then find $P(A \cup B)$.

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