Alice tosses a fair coin, then rolls a fair die. If the result is <=2, she tosses fair coin ,otherwise she tosses an unfair coin(80% gets head). .what is the probability that she gets exactly one H in two tosses?
Here's my thought. I want one h in two tosses, so first tosses she got 1/2 H or 1/2 T. If she got H, second tosses has to be T. And in second tosses, she gets 2/6 to have fair coin, and 4/6 chances to get unfair coin.
So toss H first, 1/2* (2/6*1/2+4/6*0.2)=0.15
If toss T first,we want second time to be H, 1/2*(2/6*1/2+4/6*0.8)=0.35
So the probability for question is 0.5?
Am I right?
It feels like i was wrong...