Answer:
P(D|A)=0.666
Step-by-step explanation:
We will use the tree diagram to understand these probabilities that is attached to the bottom of this answer.
Since there are three coins in the box, the probability of taking one in particular (the double-headed one, which is event D) is one third, which is equal to 0.333
Since the coin showed heads, the probability of it being a double-tailed coin is zero.
The Bayes theorem says that P(D|A) is the multiplication of P(D) and P(A), divided the probability of A happening by any means, happening D or not, which is the sum of all probabilities of A happening:
