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, find the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H?

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, find the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H, and H? 

(GATE 2017) 

Answer: 0.5 

Explanation: 

Here, the probability of getting one H is $= \dfrac{1}{2}$. 

The probability of getting (H, H, H) is 

$= \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}$ 

$= \dfrac{1}{16}$ 

The probability of getting (H, H, H, H) is 

$= \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}$ 

$= \dfrac{1}{32}$ 

Therefore, the required probability is 

$= \dfrac{\dfrac{1}{16}}{\dfrac{1}{8}}$ 

$= \dfrac{1}{2}$ 

$= 0.5$ 

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