MathematicsQ51–51 of 87 questions
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MathematicsEasyMCQTS EAMCET · 2010
Suppose $A$ and $B$ are two events such that $P(A \cap B) = \frac{3}{25}$ and $P(B - A) = \frac{8}{25}$. Then,$P(B)$ is equal to
A
$\frac{11}{25}$
B
$\frac{3}{11}$
C
$\frac{1}{11}$
D
$\frac{9}{11}$
Solution
(A) Given that $P(A \cap B) = \frac{3}{25}$ and $P(B - A) = \frac{8}{25}$.
From the properties of sets and probability,the event $B$ can be expressed as the union of two disjoint sets: $(B - A)$ and $(A \cap B)$.
Therefore,$P(B) = P(B - A) + P(A \cap B)$.
Substituting the given values:
$P(B) = \frac{8}{25} + \frac{3}{25} = \frac{11}{25}$.
From the properties of sets and probability,the event $B$ can be expressed as the union of two disjoint sets: $(B - A)$ and $(A \cap B)$.
Therefore,$P(B) = P(B - A) + P(A \cap B)$.
Substituting the given values:
$P(B) = \frac{8}{25} + \frac{3}{25} = \frac{11}{25}$.
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