Question

question 4
which of the following statements is incorrect?
the science that deals with the nature of randomness is called probability theory.
probabilities cannot exceed 1.
the probability of an event is always equal to the conditional probability of the event given a condition.
to calculate the probability of an event, the denominator is the total number of all possible outcomes.

Explanation:

The probability of an event is not always equal to its conditional probability given a condition. Conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$ (where $P(B)> 0$) and is different from the non - conditional probability $P(A)$ in most cases. The first statement correctly defines probability theory. Probabilities range from 0 to 1, so they cannot exceed 1. The formula for basic probability $P(A)=\frac{n(A)}{n(S)}$ where $n(S)$ is the total number of all possible outcomes.

Answer:

The probability of an event is always equal to the conditional probability of the event given a condition.