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Question

A and B are events with P(A) = 0.5, P(B) = 0.4 and P(AB)=0.3. Find the probability that:
(i) A does not occur
(ii) Neither A and nor B occurs

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Solution

Given:-
P(A)=0.5
P(B)=0.4
P(AB)=0.3
To find:-
(i) P(¯A)=?
(ii) P(¯A+¯B) = ?$
Solution:-
  • (i) Probability of A does not occur-
P(¯A)=1P(A)=10.5=0.5
  • (ii) Probability of neither A nor B occurs-
P(¯A¯B)=P(¯¯¯¯¯¯¯¯¯¯¯¯¯¯AB)=1P(AB)
Now as we know that,
P(AB)=P(A)+P(B)P(AB)
P(AB)=0.5+0.40.3=0.6
Therefore,
P(¯A¯B)=1P(AB)=10.6=0.4

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