An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials:
$$\text{(1) HTHTHT}\quad\text{(2) TTHHHT}\quad\text{(3) HTTHHT}\quad\text{(4) HHHT_ _}$$
Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?(A) Two $\text T$ will occur.
(B) One $\text H$ and one $\text T$ will occur.
(C) Two $\text H$ will occur.
(D) One $\text H$ will be followed by one $\text T$.
I think option A is correct and the reason is statistical regularity. Am I correct? If not then please help me how to do this problem. Any help would be appreciated. Thanks in advance.
Best Answer
$B$ is correct here. It has probability $\frac12$ in contrast to the other options that all have probability $\frac14$.
A) TT has probability $\frac14$
B) HT or TH has probability $\frac14+\frac14$ (summation of two probabilities of mutually exclusive events)
C) HH has probability $\frac14$
D) HT has probability $\frac14$
Essential for this conclusion is the fact that the coin is unbiased.