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JEE Mains · Maths · STD 11 - 14. probability
\(A , B, C\) try to hit a target simultaneously but independently. Their respective probabilities of hitting targets are \(\frac{3}{4},\frac{1}{2},\frac{5}{8}\). The probability that the target is hit by \(A\) or \(B\) but not by \(C\) is
- A \(21/64\)
- B \(7/8\)
- C \(7/32\)
- D \(9/64\)
Answer & Solution
Correct Answer
(A) \(21/64\)
Step-by-step Solution
Detailed explanation
\(P(\text { A or } B \text { but not by } C)=P((A \cup B) \cap \bar{C})\) \(=P(A \cup B) \times P(\bar{C})\) \(=[\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})] \times \mathrm{P}(\overline{\mathrm{C}})\) \(=\)…
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