Question
Download Solution PDFIf
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Complement of an event:
The complement of an event is the subset of outcomes in the sample space that are not in the event.
The probability of the complement of an event is one minus the probability of the event.
P (A̅) = 1 - P (A) ⇒ P (A) = 1 - P (A̅)
Formula: P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
Calculation:
Given:
So, P(A) = 1 - P (A̅) =
As we know, P (A ∪ B) = P (A) + P (B) - P (A ∩ B)
⇒ P (A ∪ B) = 1 - P (A̅) + P (B) - P (A ∩ B)
Hence option 1 is true.
P(A ∩ B) = P(A) P(B) =
Hence option 2 is also true.
P(A) + P(B) =
Hence option 3 is not true.
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