Question 1

What is probability?

Accepted Answer

Probability is a number between 0 and 1 that measures how likely an event is to occur. 0 means impossible; 1 means certain. We calculate it as: P(event) = favorable outcomes / total outcomes for equally-likely outcomes.

Question 2

What is the difference between permutation and combination?

Accepted Answer

Permutation counts ordered arrangements (order matters): nPr = n!/(n-r)!. Combination counts unordered selections (order doesn't matter): nCr = n!/(r!(n-r)!). If rearranging the selected items gives a different valid outcome, use permutation; otherwise use combination.

Question 3

What is expected value?

Accepted Answer

Expected value E(X) = Σ x·P(x) is the theoretical long-run average of a random variable. A fair die has E(X) = 3.5. A game with positive expected value favors the player on average; negative expected value favors the house.

Question 4

What is Bayes' theorem?

Accepted Answer

Bayes' theorem updates probabilities when new evidence is observed: P(H|E) = P(E|H)·P(H) / P(E). It is used in medical testing, spam filters, and machine learning. Key insight: even an accurate test can have mostly false positives if the condition is rare (base rate fallacy).

Question 5

What is conditional probability?

Accepted Answer

P(A|B) is the probability of event A given that event B has already occurred: P(A|B) = P(A∩B)/P(B). It restricts the sample space to only outcomes where B occurred.

Question 6

What are the basic rules of probability?

Accepted Answer

Five core rules: (1) Complement: P(not A) = 1−P(A). (2) Addition: P(A∪B) = P(A)+P(B)−P(A∩B). (3) Multiplication: P(A∩B) = P(A)·P(B|A). (4) Conditional: P(A|B) = P(A∩B)/P(B). (5) Bayes: P(H|E) = P(E|H)·P(H)/P(E).

Question 7

How do I convert odds to probability?

Accepted Answer

Fractional odds A/B: p = B/(A+B). Decimal odds D: p = 1/D. American odds +M: p = 100/(M+100). American odds −M: p = M/(M+100). Reverse: odds = p/(1−p).

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