JEE Mains · Maths · STD 11 - 14. probability
Two dice are thrown independently. Let \(A\) be the event that the number appeared on the \(1^{\text {st }}\) die is less than the number appeared on the \(2^{\text {nd }}\) die, \(B\) be the event that the number appeared on the \(1^{\text {st }}\) die is even and that on the second die is odd, and \(C\) be the event that the number appeared on the \(1^{\text {st }}\) die is odd and that on the \(2^{\text {nd }}\) is even. Then
- A the number of favourable cases of the event \((A \cup B) \cap C\) is \(6\)
- B \(A\) and \(B\) are mutually exchusive
- C The number of favourable cases of the events \(A , B\) and \(C\) are \(15,6\) and \(6\) respectively
- D \(B\) and \(C\) are independent
Answer & Solution
Correct Answer
(A) the number of favourable cases of the event \((A \cup B) \cap C\) is \(6\)
Step-by-step Solution
Detailed explanation
\(A\) : no. on \(1^{\text {st }}\) die < no. on \(2^{\text {nd }}\) die \(A\) : no. on \(1^{\text {st }}\) die \(=\) even and no. of \(2^{\text {nd }}\) die \(=\) odd \(C :\) no. on \(1^{\text {ti }}\) die \(=\) odd and no. on \(2^{\text {nd }} d i e=\) even…
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