Probability
Conditional Probability
Grade 12
Question:
<p>The boy comes from a family of two children; What is the probability that the other child is his sister?</p>
<p>(a) \(\frac{1}{2}\)</p>
<p>(b) \(\frac{1}{3}\)</p>
<p>(c) \(\frac{2}{3}\)</p>
<p>(d) \(\frac{1}{4}\)</p>
Step-by-Step Solution
Key Concept: Use conditional probability and correct sample space identification when one child is known to be a boy.
<p>Given: A boy exists in a family of two children. We need to find the probability that the other child is a girl.</p><p>Sample space (considering order): {BB, BG, GB, GG}</p><p>Given one child is a boy, the possible outcomes are: {BB, BG, GB}</p><p>Favorable outcomes (other child is a girl): {BG, GB}</p><p>Probability = $\frac{2}{3}$</p>
Correct Answer: a