Question

Find the indicated probability.

If P(A and B)=0.4, P(A) = 0.7, and

P(B) = 0.6, find P(A or B).

Answer 1

The probability of either event A or event B occurring is found using the formula P(A OR B) = P(A) + P(B) - P(A AND B). The answer is P(A OR B) = 0.9.

Step-by-step explanation:

The student is asking to find the probability of either event A or event B occurring, given the individual probabilities of each event and the combined probability of both events happening together. This probability can be found using the formula for the probability of the union of two events: P(A OR B) = P(A) + P(B) - P(A AND B).

Using the values provided:

P(A) = 0.7

P(B) = 0.6

P(A AND B) = 0.4

Plugging these into the formula gives us:

P(A OR B) = 0.7 + 0.6 - 0.4 = 0.9

Therefore, the probability that either event A or event B occurs is 0.9.

Answer 2

P(A or B) = 0.9.

Step-by-step explanation:

This is a question of Venn probabilities.

We use the following relation to solve this question.

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

The exercise states that:

`P(A) = 0.7, P(B) = 0.6, P(A \cap B) = 0.4`

Then

`P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.7 + 0.6 - 0.4 = 0.9`

The answer is:

P(A or B) = 0.9.