# Conditional and unconditional probabilities

CFA level I / Quantitative Methods: Basic Concepts / Probability Concepts / Conditional and unconditional probabilities

The unconditional probability of an event is the probability of an event without any conditions or the actual probability of occurrence of an event.

Let us try to understand this with the help of an example. Suppose the percentage change in the market price of a share is dependent on the occurrence of an event (subsidies given by the government to the company). If the event occurs i.e. the subsidies are given to the company, then the probability that the stock price will increase in next year is 80 percent. If the event does not occur, then the probability that the stock price will increase in next year is 30 percent. The probability of occurrence of the event is 40 percent. Therefore, the probability of non-occurrence of the event is 60 percent.

So, we can calculate the expected change in the stock price using probabilities.

Expected percentage change in stock price = (Probability of stock price going up next year)*(Probability of occurrence of event) + (Probability of stock price going up next year)*(Probability of not occurrence of event) = 0.80*0.40 + 0.30*0.60 = 0.32 + 0.18 = 0.50 = 50 percent.

The 50 percent number is based on the unconditional probability. It is the probability of the stock price going up next year irrespective of the fact whether the event occurs or not.

The conditional probability is dependent on some condition i.e. the probability of an event given that some other event has already happened. If in the above example, we need to calculate the percentage change in the stock price given that the event of providing subsidies to the company has already occurred, then we get the probability of stock price going up 80 percent. The 80 percent number is based on the conditional probability.

Conditional probability is denoted as P(A|B) i.e. the probability of event A given that the event B has already occurred.

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