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Class 12 Probability · Short Answer2 Marksindependent_trials

Class 12 Maths · Probability · Short Answer #45

At a crossing, independently on each day, P(green)=0.3. Find P(exactly two green days out of three, with those two consecutive).

✅ Step-by-Step Solution

Final Answer: 63/500=0.126
  1. The qualifying patterns are GGN and NGG, where N means not green; GNG is not consecutive and GGG is excluded by “exactly two”.
  2. By independence, each pattern has probability (0.3)²(0.7)=0.063; the patterns are disjoint.
  3. The required probability is 2·0.063=0.126=63/500. If three green days were also allowed, it would instead be 0.153.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] The qualifying patterns are GGN and NGG, where N means not green; GNG is not consecutive and GGG is excluded by “exactly two”.
  • [1 mark] By independence, each pattern has probability (0.3)²(0.7)=0.063; the patterns are disjoint.
  • [0.5 marks] The required probability is 2·0.063=0.126=63/500. If three green days were also allowed, it would instead be 0.153.

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