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?
The probability of getting 3 heads in 3 tosses of a fair coin is: \(0.5\times0.5\times0.5=0.125\) The probability of selecting a fair coin and getting 3 heads in 3 tosses is: \(0.99\times0.125=0.12375\)
The probability of selecting a double-headed coin and getting 3 heads in 3 tosses is: \(0.01\times1=0.01\) 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
