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