Two students Anil and Ashima appeared for examination. The probability that Anil will pass is 0.05 and that Ashima will pass is 0.10 .The probability that both will pass the exam is 0.02 .Find the probability that :

a) both anil and ashima will pass

b) atleast one of them will not pass the exam

c) only one tf them will qualify the exam

Let E and F denote the events that Anil and Ashima will pass the examination respectivelythen,PE = 0.05PF = 0.10PEF = 0.02Let E'and F' denote the events that Anil and Ashima will not qualifya   We have to find PE' F'By Demorgan's law we know that E' F' = EF' Therefore, PE' F' = PEF'PE' F' = 1 - PEF      ..............(1)Now, PEF = PE + PF - PEFor PEF = 0.05 + 0.10 - 0.02 = 0.13      ..............(2)From (1) and (2)PE' F' = 1 - 0.13 = 0.87(b)   P (Atleast one of them will not pass the examination)= 1 - P(Both of them will pass the examination)= 1 - 0.02 = 0.98(c)   P(Only one of them will qualify the examination)=PEF' + PE' F=PE - PEF + PF - PEF          as, PAB' =PA - PAB= 0.05 - 0.02 + 0.10 - 0.02= 0.15 - 0.04= 0.11        

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