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Class 12 Probability · Short Answer2 Marksprobability_distributions

Class 12 Maths · Probability · Short Answer #49

Draw two chocolates uniformly without replacement from 2 milk and 4 dark chocolates. Find the distribution of milk count X and its most likely value.

✅ Step-by-Step Solution

Final Answer: P(X=0,1,2)=(2/5,8/15,1/15); mode=1
  1. X can be 0,1,2; the sample has C(6,2)=15 equally likely pairs.
  2. Counts are C(4,2)=6, C(2,1)C(4,1)=8 and C(2,2)=1. Divide by 15 to get (6/15,8/15,1/15), summing to 1.
  3. Thus P(X=0,1,2)=(2/5,8/15,1/15). The largest probability is 8/15 at X=1: one of each type.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] X can be 0,1,2; the sample has C(6,2)=15 equally likely pairs.
  • [1 mark] Counts are C(4,2)=6, C(2,1)C(4,1)=8 and C(2,2)=1. Divide by 15 to get (6/15,8/15,1/15), summing to 1.
  • [0.5 marks] Thus P(X=0,1,2)=(2/5,8/15,1/15). The largest probability is 8/15 at X=1: one of each type.

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