Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
Assume that the birth of a boy or girl to a couple to be equally likely, and exhaustive. For a couple having $6$ children, the probability that their "three oldest are boys" is $p$ then the value of $10p$.
Step-by-Step Solution
Key Concept: The event 'three oldest are boys' is independent of the genders of the three youngest children, so we only need to calculate the probability for those three specific positions.
For a couple having 6 children, we need to find the probability that the three oldest children are all boys. Since each child's gender is independent with probability $\frac{1}{2}$ for boy and $\frac{1}{2}$ for girl, and the genders of the three youngest children don't affect this event, the probability that the three oldest are boys is $P(\text{3 oldest are boys}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8}$. Therefore $p = \frac{1}{8}$, and $10p = 10 \times \frac{1}{8} = \frac{10}{8} = 1.25$.
Correct Answer: 1.25