If $ \mathrm{A} $ and $ \mathrm{B} $ are any two events such that $ P(A)=\frac{2}{5} $ and $ P(A \cap B)=\frac{3}{20} $, then the conditional probability, $ P\left(A \mid\left(A^{\prime} \cup B^{\prime}\right)\right) $, where $ \mathrm{A}^{\prime} $ denotes the complement of $ \mathrm{A} $, is equal to :

Question

If $ \mathrm{A} $ and $ \mathrm{B} $ are any two events such that $ P(A)=\frac{2}{5} $ and $ P(A \cap B)=\frac{3}{20} $, then the conditional probability, $ P\left(A \mid\left(A^{\prime} \cup B^{\prime}\right)\right) $, where $ \mathrm{A}^{\prime} $ denotes the complement of $ \mathrm{A} $, is equal to :, $ \frac{11}{20} $, $ \frac{5}{17} $, $ \frac{\frac{3}{\tilde{n}}}{1} $, $ \frac{1}{4} $

MARKS App · Accepted Answer

Given P A = 2 5 = 8 20 & P A ∩ B = 3 20 ∴ P A ' ∪ B ' = P A ∩ B ' = 1 - P A ∩ B = 1 - 3 20 = 17 20 P A ∩ A ' ∪ B ' = P A ∩ B ' = P A - P A ∩ B = 8 20 - 3 20 = 5 20 ∴ P A A ' ∪ B ' = P A ∩ A ' ∪ B ' P A ' ∪ B ' = 5 20 17 20 = 5 17

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