Question

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed $ 6 $ times. What are possible values of x?
A. $ 9,7,4,0 $
B. $ 0,2,4,6 $
C. $ 6,7,7,2 $
D. $ 6,4,2,0 $

Answer 1

Hint: Here we will find the combinations of heads and tail when tossed six times and its difference. The difference will be calculated under mode. And then will find the possible outcomes from the possible combinations.

Complete step-by-step answer:
Let the Head of the coin be represented by “H” and the tail of the coin be represented by “T”.
“X” represents the difference between the number of heads and the number of tails.
There are a total seven combinations of the head and the tail.
 $ \therefore X(6H,0T) = \left| {6 - 0} \right| = 6 $
Similarly,
 $\therefore X(5H,1T) = \left| {5 - 1} \right| = 4 $
 $ \therefore X(4H,2T) = \left| {4 - 2} \right| = 2 $
 $ \therefore X(3H,3T) = \left| {3 - 3} \right| = 0 $
 $ \therefore X(2H,4T) = \left| {2 - 4} \right| = 2 $
In mode, when we take out negative sign outside then it is always positive.
 $ \therefore X(1H,5T) = \left| {1 - 5} \right| = 4 $
 $ \therefore X(0H,6T) = \left| {0 - 6} \right| = 6 $
Thus, the possible values of “X” are $ 0,2,4,6 $
Hence from the given multiple choices- the option B is the correct answer.
So, the correct answer is “Option B”.

Note: When any value is calculated under the modes, then the resultant values after calculation will always be positive regardless of any sign inside the modes. Find all the possible combinations of the head and tail when tossed six times.