According to MathStackExchange ---> Answered here
"Apparently the answer is 1/2 by an argument which looks like this, Since Alice tosses one more coin that Bob, it is impossible that they toss both the same number of heads and the same number of tails. So Alice tosses either more heads than Bob or more tails than Bob (but not both). Since the coins are fair, these events are equally likely by symmetry, so both events have probability 1/2."
EITHER BOB TOSSES MORE
or ALICE TOSSES MORE
so its 1/2
Draw two lines
there is one point of intersection
Draw 3 lines, there is 3 points of intersections
Draw 4 lines, there is 6 points of intersections
Draw 5 lines, there is 10 points of intersection
List:
Number of lines | Number of Intersections | Rule or Pattern |
2 | 1 | +1 |
3 | 3 | +2 |
4 | 6 | +3 |
5 | 10 | +4 |
6 | 15 | +5 |
7 | 21 | +6 |
8 | 28 | +7 |
Answer | should be | 28 |
Don't trust me, I might've gotten it wrong.