An automated safety monitoring system in an industrial plant tracks three types of potential malfunctions: overheating (event AAA), pressure spikes (event BBB), and power surges (event CCC).
For a specific production cycle, it is known that:
P(A)=0.5,P(B)=0.4andP(A∩B)=0.15 P(A) = 0.5, \quad P(B) = 0.4 \quad \text{and} \quad P(A \cap B) = 0.15 P(A)=0.5,P(B)=0.4andP(A∩B)=0.15Find
P(A∪B)P(A \cup B)P(A∪B)
P(B′∣A′)P(B' | A')P(B′∣A′)
The probability of a power surge occurring during the cycle is P(C)=0.3P(C) = 0.3P(C)=0.3.
The occurrences of overheating (AAA) and power surges (CCC) are mutually exclusive. The occurrences of pressure spikes (BBB) and power surges (CCC) are independent events.
Find P(B∩C)P(B \cap C)P(B∩C)
Describe the configuration of a Venn diagram representing events A,B,A, B,A,B, and CCC and state the probabilities associated with each of the six distinct regions.
Determine P((B∪C)′)P((B \cup C)')P((B∪C)′)
