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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

The probability that at least one of the two events A and B occurs is 0.6.If A and B occur simultaneously with probability 0.3,evaluate $P(\bar{A})+P(\bar{B})$.

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A)

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Toolbox:
  • P(at least one of A and B occeure)=P(A\(\cup\)B)                 \(Also\;\overline{A\cup\;B}=\bar{A}\cap\;\bar{B}\)
  • P(simultuneous occurance of AandB)=P(A\(\cap\)B)           \(Also\;\overline{A\cap\;B}=\bar{A}\cup\;\bar{B}\)
P(A\(\cap\)B)=0.6
P(\(\overline{A\cup\;B}\))=1-0.6=0.4
P(\(\bar{A}\)\(\cap\)\(\bar{B}\))=0.4
P(A\(\cap\)B)=0,3
P(\(\overline{A\cap\;B}\))=1-0.3=0.7
P(\(\bar{A}\cup\)\(\bar{B}\))=P(\(\bar{A}\))+P(\(\bar{B}\))-P(\(\bar{A}\)\(\cap\)\(\bar{B}\))
0.7=P(\(\bar{A}\))+P(\(\bar{B}\))-0.4
P(\(\bar{A}\))+P(\(\bar{B}\))=1.2

 

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