NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability - Exercise 13.2
Question 5

Question. 5

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is \(\dfrac{1}{4}\). Is this correct? Justify your answer.

Answer:

False

Detailed Answer with Explanation:

Step 1: Each child can be either a boy (B) or a girl (G). So there are 2 choices for each child.

Step 2: For 3 children, the total number of possible outcomes is \(2^3 = 8\).

These outcomes are: BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG.

Step 3: Count how many outcomes have:

  • 0 girls: only BBB → 1 outcome
  • 1 girl: BBG, BGB, GBB → 3 outcomes
  • 2 girls: BGG, GBG, GGB → 3 outcomes
  • 3 girls: GGG → 1 outcome

Step 4: Probability = (favourable outcomes) ÷ (total outcomes).

  • P(0 girls) = \(\tfrac{1}{8}\)
  • P(1 girl) = \(\tfrac{3}{8}\)
  • P(2 girls) = \(\tfrac{3}{8}\)
  • P(3 girls) = \(\tfrac{1}{8}\)

Step 5: Clearly, these probabilities are not equal. They are different fractions, not all \(\tfrac{1}{4}\).

Final Answer: The statement is false because the number of girls follows the binomial distribution and the probabilities are unequal.

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