Question

Two coins are in a hat. The coins look alike, but one coin is fair (with probability 1/2 of Heads), while the other coin is biased, with probability 1/4 of Heads. One of the coins is randomly pulled from the hat, without knowing which of the two it is. Call the chosen coin "Coin C". Coin c is tossed twice, showing heads both times. Given this information, what is the probability that coin c is the fair coin?

Answer 1

Answer:

0.8 or 80%

Step-by-step explanation:

The probability that the fair coin was picked and then tossed twice showing heads both times is:

$P(F) = 0.5*0.5^2\\P(F)=0.125$

The probability that the biased coin was picked and then tossed twice showing heads both times is:

$P(B) = 0.5*0.25^2\\P(B)=0.03125$

Therefore, the probability that the chosen coin is the fair coin is:

$P(C=F) = \frac{P(F)}{P(F)+P(B)}=\frac{0.125}{0.125+0.03125} \\P(C=F) = 0.8 = 80\%$

The probability is 0.8 or 80%