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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Probability

NDA 2019 · Mathematics · Probability

If A, B, C are three events, then what is the probability that at...

If A, B, C are three events, then what is the probability that at least two of these events occur together?

Options

  1. AP(A∩B)+P(B∩C)+P(C∩A)\mathrm{P}(\mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} \cap \mathrm{C})+\mathrm{P}(\mathrm{C} \cap \mathrm{A})
  2. BP(A∩B)+P(B∩C)+P(C∩A)−P(A∩B∩C)\mathrm{P}(\mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} \cap \mathrm{C})+\mathrm{P}(\mathrm{C} \cap \mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})
  3. CP(A∩B)+P(B∩C)+P(C∩A)−2P(A∩B∩C)\mathrm{P}(\mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} \cap \mathrm{C})+\mathrm{P}(\mathrm{C} \cap \mathrm{A})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})
  4. DP(A∩B)+P(B∩C)+P(C∩A)−3P(A∩B∩C)\mathrm{P}(\mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} \cap \mathrm{C})+\mathrm{P}(\mathrm{C} \cap \mathrm{A})-3 \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})

Correct answer

C. P(A∩B)+P(B∩C)+P(C∩A)−2P(A∩B∩C)\mathrm{P}(\mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} \cap \mathrm{C})+\mathrm{P}(\mathrm{C} \cap \mathrm{A})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})

Step-by-step solution

P(A∩B)+P(B∩C)+P(A∩C)−2P(A∩B∩C)\mathrm{P}(\mathrm{A} \cap \mathrm{B})+\mathrm{P}(\mathrm{B} \cap \mathrm{C})+\mathrm{P}(\mathrm{A} \cap \mathrm{C})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})
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