Question 1186366: A box contains a normal coin and a two headed coin. A coin is selected at random and tossed. If
heads appear, the other coin is tossed, if tails appear, the same coin is tossed.
(a) Find the probability that heads appear on the second toss.
(b) If heads appeared on the second toss, find the probability that it also appeared on the first toss
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! If the normal coin was picked (with probability 0.5), then the probability for heads is 0.5, after which the 2-headed coin is tossed, whose prob'y for heads is 1.
The prob'y for this event is 0.5*0.5*1 = . On the other hand, if tails turned up in the 1st toss, then the same coin is tossed, whose prob'y for heads is again 0.5.
The prob'y for heads in the 2nd toss is thus 0.5*0.5*0.5 =  .
If the 2-headed coin was picked, the prob'y for heads is 1, after which the normal coin is tossed, whose prob'y for heads is 0.5.
The prob'y for heads on the 2nd toss is thus 0.5*1*0.5 = .
Adding these probabilities up, the prob'y for heads on the 2nd toss is thus  .
The prob'y that it was heads on the 1st toss given the 2nd toss was heads is P(heads on 1st and 2nd tosses)/P(heads on 2nd toss) = 
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