Probability and Its Business Applications
Probability quantifies business risk and supports decisions under uncertainty. The exam tests sample spaces, the addition and multiplication rules, conditional probability, independence and expected value in contexts such as defects, sales outcomes and insurance.
Core rules
- For equally likely outcomes, P(A) = number favourable / total. 0 ≤ P(A) ≤ 1 and P(A′) = 1 − P(A).
- Addition: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events the intersection term is zero.
- Multiplication: P(A ∩ B) = P(A)P(B|A). If A and B are independent, P(A ∩ B) = P(A)P(B).
- Conditional probability: P(A|B) = P(A ∩ B)/P(B), provided P(B) > 0.
- Expected value E(X) = ΣxP(x), the long-run average payoff used in decision-making.
Worked example
In a customer survey, 60% buy product A, 50% buy B and 30% buy both. Then P(A ∪ B) = 0.60 + 0.50 − 0.30 = 0.80, so 80% buy at least one. Given that a customer buys B, P(A|B) = 0.30/0.50 = 0.60. The events are independent because P(A)P(B) = 0.60 × 0.50 = 0.30 = P(A ∩ B). If a salesperson earns ₹100 for each customer buying at least one product and ₹20 otherwise, expected earnings per customer are 0.80(100) + 0.20(20) = ₹84.
Traps
- Adding probabilities of events that are not mutually exclusive without subtracting the overlap.
- Confusing independence with mutual exclusivity; mutually exclusive events with positive probabilities are not independent.
- Using the wrong denominator in conditional probability.
- For “at least one”, forgetting the complement and double-counting.