Question

Suppose a box contains a double-headed coin, a double-tailed coin, and a conventional coin. A coin is picked at random and flipped; the result is a head. What is the probability it is a double-headed coin Let D = event that the coin is double-headed Let A = event that the coin shows a head Calculate P[D|A] =?

Answer 1

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:

$P(D|A)=\frac{P(D)*P(A_1)}{P(D)*P(A_1)+P(E)*P(A_2)} =\frac{0.333*1}{0.333*1+0.333*0.5}=0.666$