Question

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H.H.H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again given the previous realizations of H, H and H. would be

• A. 0.5

Answer 1

The correct option is A 0.5

1. of getting (H.H.H)
   $=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{8}$
   
   of getting (H.H.H.H)
   
   $=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{16}$
   
   $\because$ Given condition is that (H.H.H) is already realized
   
   Conditional probability of getting next H after (H.H.H)
   
   $=\frac{\frac{1}{16}}{\frac{1}{8}}=0.5$
   
   Method II:
   
   $\because$ Trials are independent so P(H in 4th trial) $=\frac{1}{2}$