21st sum plz

Asked by lovemaan5500 | 3rd Oct, 2019, 05:46: AM

Expert Answer:

Let A be an event of A speaking truth and B be the event of B speaking truth
P left parenthesis A right parenthesis equals 2 over 3 space rightwards double arrow P left parenthesis A apostrophe right parenthesis equals 1 third
P left parenthesis B right parenthesis equals 4 over 5 rightwards double arrow P left parenthesis B apostrophe right parenthesis equals 1 fifth
N o w comma space b o t h space o f space t h e m space a g r e e space i n space 2 space w a y s
1. space W h e n space b o t h space a r e space l y i n g space
2. space W h e n space b o t h space s p e a k s space t h e space t r u t h
S o comma space t h e space p r o b a b a l i t y space o f space b o t h space l y i n g space left parenthesis t h e space b a l l space d r a w n space f r o m space t h e space b a g space i s space n o t space b l a c k comma space b u t space t h e y space a r e space s a y i n g space i t space i s space b l a c k right parenthesis
equals 1 third cross times 1 fifth cross times 5 over 6

P r o b a b i l i t y space o f space b o t h space s p e a k s space t r u t h equals 2 over 3 cross times 4 over 5 cross times 1 over 6
S o comma space t h e space p r o b a b i l i t y space t h a t space t h e space s t a t e m e n t s space a r e space t r u e equals fraction numerator 2 over 3 cross times 4 over 5 cross times 1 over 6 over denominator open parentheses 2 over 3 cross times 4 over 5 cross times 1 over 6 close parentheses plus open parentheses 1 third cross times 1 fifth cross times 5 over 6 close parentheses end fraction equals fraction numerator 8 over denominator 8 plus 5 end fraction equals 8 over 13
H e n c e comma space t h e space p r o b a b i l i t y space t h a t space t h e space s t a t e m e n t s space a r e space t r u e space i s space 8 over 13.

Answered by Renu Varma | 3rd Oct, 2019, 10:14: AM