MHT CET · Maths · Probability
Given \(P(A)=0.5, P(B)=0.4, P(A \cap B)=0.3\),
then \(P\left(A^{\prime} / B^{\prime}\right)\) is equal to
- A \(1 / 3\)
- B \(1 / 2\)
- C \(2 / 3\)
- D \(3 / 4\)
Answer & Solution
Correct Answer
(C) \(2 / 3\)
Step-by-step Solution
Detailed explanation
\(P\left(A^{\prime} \mid B^{\prime}\right)=\frac{P\left(A^{\prime} \cap B^{\prime}\right)}{P\left(B^{\prime}\right)} \)
\( =\frac{P(A \cup B)^{\prime}}{P\left(B^{\prime}\right)} \)
\( =\frac{1-P(A \cup B)}{1-P(B)} \)
\( =\frac{1-[P(A)+P(B)-P(A \cap B)]}{1-P(B)} \)
\( =\frac{1-[0.5+0.4-0.3]}{1-0.4} \)
\( =\frac{0.4}{0.6} \)
\( =\frac{2}{3}\)
\( =\frac{P(A \cup B)^{\prime}}{P\left(B^{\prime}\right)} \)
\( =\frac{1-P(A \cup B)}{1-P(B)} \)
\( =\frac{1-[P(A)+P(B)-P(A \cap B)]}{1-P(B)} \)
\( =\frac{1-[0.5+0.4-0.3]}{1-0.4} \)
\( =\frac{0.4}{0.6} \)
\( =\frac{2}{3}\)
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