Question

Suppose that we have a sample space S {E₁, E₂, E₃, E₄, E₅, E₆, E₇}, where E₁, E₂, ..., E₇ denote the sample points. The following probability assignments apply:

P(E₁) = 0.05, P(E₂) = 0.15, P(E₃) = 0.1, P(E₄) = 0.25, P(E₅) = 0.1, P(E₆) = 0.1, and P(E₇) = 0.25.
Assume the following events when answering the questions. A = {E₁, E₄, E₆} B = {E₂, E₄, E₇} C = {E₂, E₃, E₅, E₇}
Find P(A).

Answer 1

The probability of event A, denoted as P(A), is 0.4.

Step-by-step explanation:

To find the probability of event A, denoted as P(A), we sum the individual probabilities of the sample points in A. Event A is defined as A = {E₁, E₄, E₆}, so we add the probabilities of these sample points: P(A) = P(E₁) + P(E₄) + P(E₆) = 0.05 + 0.25 + 0.1 = 0.4. Therefore, the probability of event A is 0.4.

In the sample space S, each sample point has an assigned probability, and events are subsets of the sample space. The probability of an event is the sum of the probabilities of its constituent sample points. In this case, event A consists of three sample points, and the probability of A is the sum of the probabilities of E₁, E₄, and E₆.

In conclusion, the probability of event A, denoted as P(A), is calculated by summing the individual probabilities of the sample points in A. This straightforward calculation provides the probability associated with the occurrence of event A within the given sample space and probability assignments.