Question

A jar contains 99% fair coins, and 1% double-headed coins. you took a coin at random, then toss it 3 times and observed 3 heads. what is the probability that you picked a double-headed coin?

Answer 1

1 in 100, because you have 99% fair coins and just 1% double-headed one, then 99 + 1 is obviously 100, so you have a 1 in 100 chance

Answer 2

The probability of getting 3 heads in 3 tosses of a fair coin is:

`0.5*0.5*0.5=0.125`
The probability of selecting a fair coin and getting 3 heads in 3 tosses is:

`0.99*0.125=0.12375`

The probability of selecting a double-headed coin and getting 3 heads in 3 tosses is:

`0.01*1=0.01`
The probability of selecting a coin and getting 3 heads in 3 tosses is:
0.12375 + 0.01 = 0.13375
The probability that a double-headed coin was picked is:
0.01/0.13375 = 0.0748

The answer is 0.0748 or 7.48%