JEE Mains · Maths · STD 11 - 14. probability
For three events \(A,B \) and \(C\) ,\(P (\) Exactly one of \(A\) or \(B\) occurs\()\, =\, P (\) Exactly one of \(C\) or \(A\) occurs \() =\) \(\frac{1}{4}\) and \(P (\) All the three events occur simultaneously \() =\) \(\frac{1}{16}\) Then the probability that at least one of the events occurs is :
- A \(\frac{3}{{16}}\)
- B \(\frac{7}{{32}}\)
- C \(\frac{7}{{16}}\)
- D \(\frac{7}{{64}}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{{16}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}\) (exactly one of \(A\) or \(B\) occurs) \(=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{4}\) ....\((1)\) \(\mathrm{P}(\text { Exactly one of } \mathrm{B} \text { or \)C\( occurs })\)…
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