If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
Select:
A) 1/16
B) 3/16
C) 1/8
D) 3/8
E) 1/2
A) 3 heads..   all three heads can be taken as one, so total are 4- 3H,T,T,T...   3H can take any of four places= 4 ways..   B) 4 Heads..   again 3H are one but it cannot have fourth one next to it..   (i)so if we have 3H in edges.. 3H,T,_,_   the last two can be H,T or T,H--- so 2 ways..   similarily if 3H in the rightmost position-- _,_,T,3H---- 2 ways..   (ii) if we have 3H in middle... T,3H,T,H and H,T,3H,T--- 2ways..   TOTAL=2+2+2= 
<gadget id="calculator">2+2+2</gadget>
<output>6</output>
6 ways..   C) 5 heads..   Again 3H in edges-- 3H,T,H,H or H,H,T,3H--2 ways.   we cannot have 3H in middle, as it will surely have a H adjacent to it, resulting in 4 H in a row..   D) 6 Heads--   NO possiblity..   TOTAL ways to have exactly 3H in a row=4+6+2= 
<gadget id="calculator">4+6+2</gadget>
<output>12</output>
12 ways..   total combinations of 6 tosses= 2^6..   Probability= 12/2^6= 3/16   Answer: 3/16.
<result>B</result>
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?