Question

Let X represents 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?

Answer 1

When a coin is tossed 6 times, possible outcomes are,

S={ ( 6T,0H ),( 5T,1H ),( 4T,2H ),( 3T,3H ),( 2T,4H ),( 1T,5H ),( 0T,6H ) }

Here,

T→Tail H→Head

Consider X be the difference between the number of heads and the number of tails

Draw a table for the different sample space:

Outcome	Number of tails	Number of heads	X: difference between number of heads and number of tails
6T,0H	6	0	6−0=6
5T,1H	5	1	5−1=4
4T,2H	4	2	4−2=2
3T,3H	3	3	3−3=0
2T,4H	2	4	4−2=2
1T,5H	1	5	5−1=4
0T,6H	0	6	6−0=6

Thus, possible values of X are 0, 2, 4 and 6.