Conditional Probabilities (p10)

One proposal for addressing climate change is to spray small reflective particles known as aerosols into the stratosphere to reflect a portion of incoming solar radiation. Volcanic eruptions, which have a similar impact over short periods of time, suggest that it could work. However, very little is known about whether the technique would be safe for long term use.

Suppose the policy would have one of two long term outcomes: good (G), under which it would reduce warming with few side effects, or bad (B), under which it would do little to reduce warming and have bad side effects. Both G and B are currently believed to be equally likely: each probability is 50%. A research project has been proposed to determine whether the outcome would be G or B before the policy is undertaken. However, the project is not infallible: there is a 10% chance that it would report that the policy would be bad (rB) when it would actually be good (G), and a 30% chance that it would report that the policy would be good (rG) when it would actually be bad (B).

Please calculate the four conditional probabilities: (1) probability of G given rG; (2) probability of B given rG; (3) probability of G given rB; and (4) probability B given rB.