Probability
Equally likely outcomes, draws from urns, unions and intersections, conditional probability, total probability and Bayes. Probability is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 6 lessons, each with the rule that solves it and a diagram.
Basic probability
With equally likely outcomes, P(A) = favourable ÷ possible. Two dice give 36 ordered pairs, and their sums are not equally likely. P(not A) = 1 − P(A): count “at least one” through “none”.
Drawing from an urn
With replacement the urn stays the same and the draws are independent; without replacement update the numerator and the denominator after each draw. Multiply along a branch, add separate branches, or count groups with combinations.
Union and intersection
P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Disjoint events cannot happen together, so their probabilities add; independent events do not influence each other, so P(A ∩ B) = P(A) · P(B).
Conditional probability
P(A | B) = P(A ∩ B) ÷ P(B): the condition becomes the new universe. In a two-way table, divide the cell by the total of the condition’s row or column. P(A | B) is usually not P(B | A).
Total probability
Split into cases that cover everything once, follow each road to the result multiplying along it, and add the roads: P(B) = Σ P(Aᵢ) · P(B | Aᵢ). The result is a weighted mean of the rates.
Bayes’ theorem
Bayes reverses a conditional probability: from P(result | cause) to P(cause | result). The answer is the branch you want divided by every branch that reaches the result.
What is the Bocconi Test format?
Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.
- Questions / time
- 50 / 75 minutes
- Distribution
- 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
- Scoring
- +1 correct · 0 blank · −0.2 wrong
- Question languages
- English · Italian
- Three-option questions
- Some critical thinking questions have three options; a wrong answer there costs −0.33
- Minimum score
- Below 17 points the test is not considered for selection
- AI degree
- Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
- Law test
- A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring
Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)
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