General ScienceMadrid 2026Question 2A
X-linked inheritance
A healthy father and a carrier mother: the Punnett square and why it comes out this way
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Problem statement
Given that $P(B) = 0.4$, $P(\overline{A\cup B}) = 0.4$ and $P(B|A) = 0.2$, calculate the following probabilities:
a) (1 mark) $P(\overline{A})$ and $P(A\cap B)$.
b) (1 mark) $P((A\cap B)|(A\cup B))$.
Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Mathematics · Question 4.2. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.What this lesson answers
- What does each piece of data say, and what can we predict?
- Why does the conditional probability give a relation and not a number?
- Why do we subtract the intersection in the union?
- Part a): which regions are we asked for?
- Part b): why does the numerator simplify?
- Another way: splitting the square into four regions
- The answers and how to check them
- Common mistakes to avoid
- Exam tips
- For top marks
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