Bayes Theorem- Please verify

[kangkan]

A bag contains six different balls of diff color. A ball is drawn at random. A speaks truth 4/7 times and B 7/10 times.IF both A and B tell that red ball wasdrawn,what is the probability that red ball was drwan

My sloutin

A:be the event that both are telling the truth
B: be the event that both are lying
C:be the event that red is repoted

P(C/A)=1/6

P(C/B)=(1/25)

Hence P(A/C)=P(C/a)*(4/7)(7/10)/{ P(c/a)*(4/7)*(7/10)+ P(C/B)*(3/7)*(3/10)

[Arushi :))]

right according to meeeeeeee