Answer :
Answer:
Therefore the probability that he was taught by method A is 0.78.
Explanation:
Probability:
The ratio of the number of favorable outcomes to the number of all possible outcomes.
Bayes' Rule:
If the events [tex]B_1[/tex],[tex]B_2[/tex], .....[tex]B_n[/tex] from a portion of a sample space S and A is any events of A, then
[tex]P(B_i|A)=\frac{P(B_i)P(A|B_i)}{\sum_{j=1}^kP(B_j)P(A|B_j)}[/tex]
Given that,
There are two available method for teaching A and B.
The failure rate for A is 35%
That is P(F|A) =35%=0.35
The failure rate for B is 15%
That is P(F|A) =15%=0.15
A used 40% of the time.
P(A)=40%=0.40
B used 60% of the time.
P(A)=60%=0.60
To find P(A|F) , we use the Bayes's rule.
[tex]P(A|F)=\frac{P(A)P(F|A)}{P(A)P(F|A)+P(B)P(F|B)}[/tex]
[tex]=\frac{0.60\times 0.35}{0.60\times 0.35+0.40\times 0.15}[/tex]
=0.78
Therefore the probability that he was taught by method A is 0.78.