Two students Anil and Ashima appeared for examination The probability that Anil will pass is 0 05 and that - Maths - Probability

Question

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

Manbar Singh · Accepted Answer

Solution :

Let E and F denote the events that Anil and Ashima will pass the examination respectivelythen,PE = 0
05PF = 0 10PE∩F = 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' = E∪F' Therefore, PE'∩ F' = PE∪F'⇒PE'∩ F' = 1 - PE∪F      
(1)Now, PE∪F = PE + PF - PE∩For PE∪F = 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)=PE∩F' + PE'∩ F=PE - PE∩F + PF - PE∩F          as, PA∩B' =PA - PA∩B= 0
05 - 0 02 + 0 10 - 0 02= 0
15 - 0 04= 0
11