JEE Mains · Maths · STD 12 - 13. probability
Let \(A\) and \(B\) be two independent events such that \(\mathrm{P}(\mathrm{A})=\frac{1}{3}\) and \(\mathrm{P}(\mathrm{B})=\frac{1}{6} .\) Then, which of the following is TRUE?
- A \(\mathrm{P}(\mathrm{A} / \mathrm{B})=\frac{2}{3}\)
- B \(\mathrm{P}(\mathrm{A} /(\mathrm{A} \cup \mathrm{B}))=\frac{1}{4}\)
- C \(\mathrm{P}\left(\mathrm{A} / \mathrm{B}^{\prime}\right)=\frac{1}{3}\)
- D \(\mathrm{P}\left(\mathrm{A}^{\prime} / \mathrm{B}^{\prime}\right)=\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{P}\left(\mathrm{A} / \mathrm{B}^{\prime}\right)=\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(\mathrm{A} / \mathrm{B})=\mathrm{P}(\mathrm{A})=\frac{1}{3}\) \(P(A /(A \cup B))=\frac{P(A \cap(A \cup B))}{P(A \cup B)}=\frac{P(A)}{P(A \cup B)}\) \(=\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{6}-\frac{1}{18}}=\frac{3}{4}\)…
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