JEE Mains · Maths · STD 11 - 14. probability
Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \(E_1\) is the event that die \(A\) shows up four, \(E_2 \) is the event that die \(B\) shows up two and \(E_3\) is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true \(?\)
- A \(E_1 \) and \(E_3 \) are independent.
- B \(E_1 , E_2\) and \(E_3 \) are independent.
- C \(E_1\)and \(E_2\) are independent.
- D \(E_2 \) and \(E_3 \) are independent.
Answer & Solution
Correct Answer
(B) \(E_1 , E_2\) and \(E_3 \) are independent.
Step-by-step Solution
Detailed explanation
\(E_{1} \rightarrow A\) shows up 4 \(\mathrm{E}_{2} \rightarrow \mathrm{B}\) shows up 2 \(E_{3} \rightarrow \operatorname{Sum}\) is odd (i.e. even \(+\) odd or odd \(+\) even) \(\mathrm{P}\left(\mathrm{E}_{1}\right)= \frac{6}{6.6}=\frac{1}{6}\)…
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