Question

the probability that event a will occur is 0.5, the probability that event b will occur is 0.6, and the probability that both event a and event b will occur is 0.4. what is the probability that neither event a nor event b will occur? competency c13

Explanation:

Step1: Find \( P(A \cup B) \)

Using the formula for the probability of the union of two events: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).
Given \( P(A) = 0.5 \), \( P(B) = 0.6 \), and \( P(A \cap B) = 0.4 \).
So, \( P(A \cup B) = 0.5 + 0.6 - 0.4 = 0.7 \).

Step2: Find the probability of neither A nor B

The probability that neither event A nor event B occurs is \( 1 - P(A \cup B) \).
Substitute \( P(A \cup B) = 0.7 \) into the formula: \( 1 - 0.7 = 0.3 \).

Answer:

\( 0.3 \)