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NDA 2020 Maths · Mathematics · Probability · easy

If P(A)=0.6, P(B)=0.3 and the events A and B are independent, then P(A∪ B) is

Single correct option

If P(A)=0.6P(A)=0.6, P(B)=0.3P(B)=0.3 and the events AA and BB are independent, then P(A∪B)P(A\cup B) is
  1. A. 0.90.9
  2. B. 0.180.18
  3. C. 0.420.42
  4. D. 0.720.72
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Answer: (D) 0.720.72

For independent events P(A∩B)=P(A)P(B)=0.18P(A\cap B)=P(A)P(B)=0.18. Then P(A∪B)=P(A)+P(B)−P(A∩B)=0.6+0.3−0.18=0.72P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.6+0.3-0.18=0.72. The value 0.90.9 simply adds the probabilities (valid only for mutually exclusive events), 0.180.18 is the intersection, and 0.420.42 results from subtracting the product twice. Equivalently 1−0.4×0.7=0.721-0.4\times0.7=0.72.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake