CONCEPT: The question is based on the concepts of Conditional Probability

SOLUTION:
 

The Probability of selecting a fair coin= 64/65

The Probability of getting 6 heads in a row with the fair coin= (1/2)^6= 1/64

The Probability of selecting the unfair 2-headed coin= 1/65

Probability of getting 6 heads in a row with the 2-headed coin= 1


If a coin, chosen at random from the bag and then tossed, turns up heads 6 times in a row, the probability that it is the two-headed coin(P (B/A))

= [(1/65)*1] / [{(64/65)*(1/64)}+{(1/65)*1}]
= (1/65)/(2/65)
= 1/2

Hence OPTION (E)