Maths · Probability: Probability of an event, addition and multiplication theorems of probability
The probability that atleast one of the events happens is If probability of thei
The probability that atleast one of the events \( A, B \) happens is \( 0.6 . \) If probability of their simultaneously happening is \( 0.5, \) then \( \boldsymbol{P}(\overline{\boldsymbol{A}})+\boldsymbol{P}(\overline{\boldsymbol{B}})= \)
- A. 0.4
- B. 0.8
- C. 0.9
- D. 1.
Step-by-step solution
Given P(A∪B)=0.6 and P(A∩B)=0.5. By inclusion-exclusion: P(A∪B)=P(A)+P(B)-P(A∩B) ⇒ 0.6=P(A)+P(B)-0.5 ⇒ P(A)+P(B)=1.1. Then P(Ā)+P(B̄)=(1-P(A))+(1-P(B))=2-(P(A)+P(B))=2-1.1=0.9.
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