Question

Use the contingency table to the right to determine the probability of events.

a. What is the probability of event A?
b. What is the probability of event A?
c. What is the probability of event A and B?
d. What is the probability of event A or B?
1. The probability of event A is.
2. The probability of event A' is
3. The probability of event A and B is
4. the probability of event A or B is

Answer 1

1. The probability of event A is 0.35.

2. The probability of event A' is 0.65.

3. The probability of event A and B is 0.15.

4. The probability of event A or B is 0.55.

Step-by-step explanation:

In the given contingency table, event A corresponds to the sum of the probabilities in the first row. Adding the values in the first row gives the probability of event A, which is 0.25 (event A in column 1) + 0.1 (event A in column 2) = 0.35.

To find the probability of event A', which represents the complement of A, subtract the probability of A from 1. Therefore, the probability of event A' is 1 - 0.35 = 0.65.

The probability of both events A and B occurring is represented by the intersection of their probabilities in the table. In this case, it is the value in the cell where the row corresponding to event A intersects with the column corresponding to event B. Thus, the probability of A and B is 0.15.

To find the probability of either event A or event B, sum the probabilities of each event individually and subtract the probability of their intersection to avoid double counting. Therefore, the probability of A or B is (0.35 + 0.25 + 0.15) - 0.15 = 0.55.