Let the probability of occurrence of first event A, be ‘a’ i.e., P(A) = a ∴ P(not A) = 1 – a And also suppose that probability of occurrence of second event B, P(B) = b, ∴ P(not B) = 1 – b Now, P(A and notB)+P(notA and B)=
26
49
⇒P(A)×P(notB)+P(notA)×P(B)=
26
49
⇒a×(1−b)+(1−a)b=
26
49
⇒a+b−2ab=
26
49
......(i) And A and notB)=
15
49
⇒P(notA)×P(notB)=
15
49
⇒(1−a)×(1−b)=
15
49
⇒1−b−a+ab=
15
49
⇒a+b−ab=
34
49
......(ii) From (i) and (ii), a+b=
42
49
.......(iii) and ab=
8
49
(a−b)2=(a+b)2−4ab=
42
49
×
42
49
−
4×8
49
=
196
2401
∴a−b=
14
49
........(iv) From (iii) and (iv), a=
4
7
,b=
2
7
Hence probability of more probable of the two events =