Question

if a fair coin is tossed 6 times what is the expected difference between number of heads and tails?

Answer 1

Answer:

The expected difference between number of heads and tails is 6, 4, 2 or 0.

Step-by-step explanation:

Given data: A fair coin has been tossed 6 times. Therefore, each toss has the possibility of 2 outcomes i.e., 1 head or 1 tail.

To find: expected difference between no. of heads and tails.

Let’s find out the no. of expected difference between the heads and tails for possible tosses:

Possibility 1:  

6 heads and 0 tail

∴ expected difference = | 6 – 0 | = 6

Possibility 2:  

5 heads and 1 tail

∴ expected difference = | 5 – 1 | = 4

Possibility 3:  

4 heads and 2 tails

∴ expected difference = | 4 – 2 | = 2

Possibility 4:  

3 heads and 3 tails

∴ expected difference = | 3 – 3 | = 0

Possibility 5:  

2 heads and 4 tails

∴ expected difference = | 2 – 4 | = 2

Possibility 6:  

1 head and 5 tails

∴ expected difference = | 1 – 5 | = 4

Possibility 7:  

0 head and 6 tails

∴ expected difference = | 0 – 6 | = 6

From the above calculations, we can say that, the expected difference between the no. of heads and tails could be 6, 4, 2 or 0.