An enzyme experiment has been performed many times with the

An enzyme experiment has been performed many times with the following probabilities calculate/noted: Probability experiment was successful = 0.70 Probability the right amount of enzyme was used given that the experiment was successful = 0.45 Probability the right amount of enzyme was used given the experiment was NOT successful = 0.20 Find the probability that the right amount of enzyme was used.

Solution

We will use Bayes theorem here according to which,

P(right amount of enzyme was used ) = P(experiment was successful)*P(right amount of enzyme was used given that experiment was successful)+ P(experiment was NOT successful)*P(right amount of enzyme was used given that experiment was NOT successful)

P(right amount of enzyme was used ) = 0.70*0.45+(1-0.70)*0.20 = 0.375