In a betting game in an exhibition two dice P and Q are being used. Dice P has four red faces and two white faces where as dice Q has two red and four white faces. A fair coin is tossed once. If it shows head the game continues by throwing dice P. If it falls tail dice Q is thrown. If first n throws of the die all turns up red then find the probability that P is being used.
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Sol. Probability of getting all red faces in throws by die P = 
.
Probability of getting all red faces i- throws by die Q = 
Probability that die P was being used = 
= 
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