We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. we choose a coin at random, toss it, and it comes heads. what is the probability that the opposite face is tails?

1/3

Step-by-step explanation:

There are 3 coins, and each coin has 2 possible outcomes.  So there are a total of 6 possible outcomes.

Of these 6 outcomes, 3 are heads.  Of these 3, only 1 has tails on the opposite face.

So the probability is 1/3.

We can also show this using conditional probability:

P(A|B) = P(A∩B) / P(B)  

Probability that A occurs, given that B has occurred = Probability that both A and B occur / Probability that B occurs

Here, A = tails on opposite face and B = heads.

P(A|B) = (1/6) / (3/6)

P(A|B) = 1/3

answer: translate the circles so they share a common center point and dilate circle y by a scale factor of 3.