Question 1186366
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 ={{{red(1/4)}}}.  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 = {{{red(1/8)}}}.

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 = {{{red(1/4)}}}. 

Adding these probabilities up, the prob'y for heads on the 2nd toss is thus {{{1/4 + 1/8 + 1/4 = red(5/8)}}}.

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) = {{{(1/4+1/4)/(5/8) = (1/2)/(5/8) = red(4/5)}}}