Question

Here are two coins in a box. one coin is fair, the other has heads on both sides. you draw one coin at random, toss it, and it lands up heads. what is the probability that you drew the two-headed coin?

Answer 1

Heads will come up when you draw the two headed coin 1/2 This 1/2 is for the draw. You have certainty of getting heads from this coin.

On a fair coin, probability of drawing the coin is 1/2
The probability of getting heads is 1/2
The probability is 1/2 * 1/2 = 1/4 with this coin

The total probability = 1/4 + 1/2 = 3/4 or 0.75 of getting heads.
Therefore the probability of drawing the 2 headed coin is 1/2 // 3/4
0.5 / 0.75 = 0.666666