Make sure you remember this week’s question before moving on to the explanation.
Question
If a fair coin is tossed six times, what is the probability of getting exactly three heads in a row?
(A) 1/16
(B) 3/16
(C) 1/8
(C) 3/8
(D) 1/2
Answer and Explanation
A good way to think about this problem is to map out a valid instance of what the question is asking for:
H H H T T T
T H H H T T
T T H H H T
We could go on like this but in doing so we might miss something. See, the thing we want to pay attention to is the word “exactly”. This means we can’t have four heads in a row.
We also have to be aware of the fact that having three heads in a row can happen in more than one way, even in the first position above (HHHTTT).
For instance, successful trials with heads in the first position consist of the following:
H H H T H T
H H H T T H
H H H T H H
It is important to remember that three heads can also come at the end, even when the first coin is heads:
H T H H H T
H T T H H H
H H T H H H
With a tails in the first position we get the following:
T H H H T T
T H H H T H
T H T H H H
T T H H H T
T T T H H H
This gives us a total of 12 possible instances out of a total of 2^6 possibilities:
12/64 = 3/16
See you again soon!