JEE Mains · Maths · STD 11 - 14. probability
Let S be a set of 5 elements and \( P(S) \) denote the power set of S. Let E be an event of choosing an ordered pair \( (A, B) \) from the set \( P(S)\times P(S) \) such that \(A \cap B=\varnothing\). If the probability of the event E is \( \frac{3^p}{2^q} \), where \( p, q \in \mathbb{N}, \) then \( p+q \) is equal to
- A 10
- B 12
- C 15
- D 18
Answer & Solution
Correct Answer
(C) 15
Step-by-step Solution
Detailed explanation
\(S=\{a, b, c, d, e\} \) \(P ( S )\) contains 32 elements both set A and set B are subsets of \(P ( S )\) Every element has 4 choices \(\text {Favourable cases }=3^5\) \(\text {Total cases }=4^5\) \(P =\frac{3^5}{4^5}=\frac{3^5}{2^{10}}\) \(m=5, n =10\) \(m+ n =15\)
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