Hint

 

 

Bounce and Skill alternately threw a stone at the coconut. The game ended as soon as one of them hit the target.

E.g. The game ended in 5 throws with Bounce winning the game:

Bounce

1st throw

Skill

2nd throw

 Bounce

3rd throw

Skill

4th throw

Bounce

5th throw

x x x x

Bounce would win the game if any of the following cases occured:

The game ended in   Click for answers  
1 throw  
3 throws x x  
5 throws x x x x  
7 throws x x x x x x  
and so on.      

 

Solution

The probability that Bounce got the coconut in the end

=P(game ended in 1 throw)+P(game ended in 3 throws)+P(game ended in 5 throws)+...

=0.2 + 0.8x0.7x0.2 + 0.8x0.7x0.8x0.7x0.2 + ...

=0.2/(1-0.8x0.7)

=5/11

Conclusion

The probabilities that Bounce and Skill got the biggest coconut were

5/11 and 6/11 respectively .

 

Answers to the previous questions:

Qu1 Will shooting first actually increase Bounce's chance of hitting the coconut?

Yes, see how significantly Bounce's chance of getting the coconut increased to 5/11 when Bounce could throw a stone first.

Qu2 Will shooting first provide Bounce a sufficient advantage to overcome his lesser skill?

No, Skill was still more likely to win the biggest coconut. But note how close the game was once Bounce had the first-mover advantage.