Question

There are two children in a family. The probability that both of them are boys is:

• A. \(\dfrac{1}{2}\)
• B. \(\dfrac{1}{3}\)
• C. \(\dfrac{1}{4}\)
• D. \(\dfrac{2}{5}\)

Hint:

For problems involving children and gender:

Assume equal probability for boy and girl unless stated otherwise
List all equally likely outcomes
Probability = (dfractextfavourable outcomestexttotal outcomes)

Answer 1

The Correct Option is C

Step 1: List all possible outcomes. Assume that the probability of having a boy or a girl is equal and independent for each child. Possible combinations for two children are: \[ \text{BB},\ \text{BG},\ \text{GB},\ \text{GG} \] Step 2: Count total and favourable outcomes.

Total possible outcomes \(= 4\)
Favourable outcome (both are boys) \(= \text{BB}\)
Step 3: Calculate the probability. \[ P(\text{both boys}) = \frac{1}{4} \] Step 4: Final conclusion. The probability that both children are boys is: \[ \boxed{\dfrac{1}{4}} \]