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CBSE Class 12 Math 2025 All Sets Solved Paper

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Question : 7 of 20
Marks: +1, -0
Let M and N be two events such that P(M) = 0.6, P(N) = 0.2 and P(M∩N)=0.5,P(M \cap N)=0.5, then P(M′N′)P\left(\frac{M'}{N'}\right) is
Solution:  
P(M)=0.6,P(N)=0.2,P(M∩N)=0.5,P(M)=0.6, P(N)=0.2, P(M \cap N)=0.5,
P(M∪N)=P(M)+P(N)−P(M∩N)P(M \cup N)=P(M)+P(N)-P(M \cap N)
P(M′N′)=  P(M′∩N′)P(N′)=  P((M∪N)′)P(N′)P\left(\frac{M'}{N'}\right) = \; \frac{P(M' \cap N')}{P(N')} = \; \frac{P((M \cup N)')}{P(N')}
=  1−P(M∪N)1−P(N)= \; \frac{1-P(M \cup N)}{1-P(N)}
=  1−[P(M)+P(N)−P(M∩N)]1−P(N)= \; \frac{1-[P(M)+P(N)-P(M \cap N)]}{1-P(N)}
=  1−[0.6+0.2−0.5]1−0.2= \; \frac{1-[0.6+0.2-0.5]}{1-0.2}
=  1−0.30.8=  0.70.8= \; \frac{1-0.3}{0.8} = \; \frac{0.7}{0.8}
=  78= \; \frac{7}{8}
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