Matiu has four coins. If he tosses them all at the same time, what is the most likely number of heads to show? What is the most likely number of tails? Is he more likely to have two heads and two tails, or different numbers of each?
Solution:
There are 16 possibilities for the results of tossing four coins. They are listed below (with the number of heads in brackets).
HHHH (4)
HHHT (3)
HHTH (3)
HHTT (2)
HTHH (3)
HTHT (2)
HTTH (2)
HTTT (1)
THHH (3)
THHT (2)
THTH (2)
THTT (1)
TTHH (2)
TTHT (1)
TTTH (1)
TTTT (0)
By counting up the possibilities with each number of heads we can see that there is 1 way to get 4 heads, 3 ways to get 4 heads, 6 ways to get 2 heads, 4 ways to get 1 head, and 1 way to get 0 heads.
So, the most likely number of heads is 2. The most likely number of tails is also 2.
Since 6 of the 16 possibilities give 2 heads, that means that 10 out of 16 give different numbers of heads and tails, so it is more likely that the numbers will be different.