I am struggling to calculate the ratios for converging connections in bayesian networks.

For example...

TBoC ---> D <--- B

This is modelled by the formula, p(D | TBoC, B).

When the TBoc and D are instantiated... p(D = yes | TBoC = yes | B),

The likelihood ratio is 90:70.

and the Priors of B are true: 45% and false: 55%.

I know the answers I am looking for are 51.266% and 43.734%, but I just can't seem to work out how to do this!

How do I work out the change in chances of the patient having Bronchitis?

Looking forward to any help,

Thanks.