Answer:
75.95% probability that he was taught by method A.
Step-by-step explanation:
We have these following probabilities:
An 80% probability of method A being used.
A 20% probability of method B being used.
If method A is used, a 75% probability of learning the skill successfully.
If method B is used, a 95% probability of learning the skill successfully.
This exercise can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
So
What is the probability of him being taught by method A, given that he learned the skill succesfully.
P(B) is the probability of being taught by method A, so P(B) = 0.80.
P(A/B) is the probability of learning the skill successfully, given that he was taught by method A. So P(A/B) = 0.75.
P(A) is the probability of learning the skill successfully. It is 75% of 80% plus 95% of 20%. So
Finally
There is a 75.95% probability that he was taught by method A.