A pharmaceutical company has two drug trials coming up. For the first trial, they project a 60% success rate. For the second trial, however, they project a 45%

Question

A pharmaceutical company has two drug trials coming up. For the first trial, they project a 60% success rate. For the second trial, however, they project a 45% success rate.

Based on these projections, what is the probability that both trials will be failures?

Answer 1

It sounds like the two trials are unrelated, in terms of probability of success. In other words, if trial 1 fails, it is no more or less likely that trial 2 will succeed. We also assume there is no other state but success or failure (no "almost" for example).

 

Since they're unrelated, and neither is given any more weight than the other, I would simply average the projected success rates to find the overall success rate. Then, the failure rate will be 1 - overall success rate. Alternatively, first find the failure rates of each, then average; it doesn't matter which you do first.

 

I get (40 + 55)/2, or 47.5%. Now do a reality check. My answer is less than 50/50 probability that both will fail. Does that seem reasonable, given the info provided? 

Answer 2

Assume each trial is independent of the other trial.

 

Let A be the event that trial 1 fails and B be the event that trail 2 fails.

 

P[A] = 1 - 0.6 = 0.4 and P[B] = 1 - 0.45 = 0.55

 

Now P[A and B] = P[A∩B] = P[A] * P[B], since the events are independent of each other.

 

 ∴P[both trials will fail] = 0.4 * 0,55 = *.22