Find conditional prob. that project does well, given that...

[ravifour]

Please help; I am struck on the following:

Suppose you are a project manager and you believe that the “espresso” project will do well with probability 0.80. Given that it does well, you believe the “herbal tea” project is likely to do well with probability 0.70. However, if the espresso project does not do well, then the herbal tea project has only a 25% chance of doing well.

a. Find the probability that the herbal tea project does well.

b. Find the conditional probability that the espresso project does well given that the herbal tea project does well.

Thanks
Ravi

 

[pka]

Here is part a.
\(\displaystyle \begin{array}{l}
P(E) = 0.8,\quad P(H|E) = 0.7\quad \& \quad P(H|E') = .25 \\
P(HE) = \left( {.75} \right)\left( {0.8} \right) \\
P(HE') = \left( {.25} \right)\left( {.2} \right) \\
P(H) = P(HE) + P(HE') \\
P(E|H) = \frac{{P(EH)}}{{P(H)}} \\
\end{array}\)

 

[ravifour]

PKA, Thank You.