Bayes' Theorem Part-4 -- Example

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Bayes’ Theorem Part-4 – Example

Assume you’re a securities analyst at an investment bank. consistent with your research of publicly-traded companies, 60% of the businesses that increased their share price by quite 5% within the last three years replaced their CEOs during the amount .

At an equivalent time, only 35% of the businesses that didn’t increase their share price by quite 5% within the same period replaced their CEOs. Knowing that the probability that the stock prices grow by quite 5% in 4%, find the probability that shares of a corporation that fires its CEO will increase by quite 5%.

Before finding the probabilities, you must first define the notation of the probabilities.

• P(A) — the probability that the stock price increases by 5%.
• P(B) — the probability that the CEO is replaced.
• P(A|B) — the probability of the stock price increases by 5% given that the CEO has been replaced.
• P(B|A) — the probability of the CEO replacement given the stock price has increased by 5%.

Using the Bayes’ theorem , we will find the specified probability:

Thus, the probability that the shares of a corporation that replaces its CEO will grow by quite 5% is 6.67% probability.