There are two coins one of which is genuine and the other co

There are two coins one of which is genuine and the other counterfeit. The real one is fair, and the false one has the probability of coming up heads 60%. You get to choose a coin uniformly and randomly among the two coins, and upon having chosen, flip it 3 times. The observed outcome is HHH. What is the probability that the chosen coin is false?

Solution

let

R is fair coin

F is false coin

then P(F)=P(R)=1/2 =0.5

H is head and T is tell

we have to find P(HHH| F)

then

   P(HHH|F)=(P(HHH and F)) / P(F)

           =(0.6)³ / 0.5

         =0.216/0.5 =0.432