Math Is Fun Forum

On a cricket pitch measuring 40*25 metres, a bowler bowls to a batsman who hits a ball at a certain speed. There are 20 'catchers' (placed at the points indicated by the diagram to the left), who each cover a small section of the pitch: What is the likelihood of the ball being caught if all of the following criteria are met:

a: the moment the ball has been hit, the catchers 'magically' know where the ball will end up, and start moving to that position at a constant speed.
b: the catchers always catch the ball if they can reach it.
c: the batter hits the ball such so that it only lands on the patterned green area, and that each 'spot' of this pitch is just as likely to be reached as any other 'spot'.
d: The ball travels at a speed of 10 metres per second.
e: The catchers run at different speeds, with the ones at the back being the slowest. Here are the speeds each row of catchers possess (mps=metres per second):
Row a: 1 mps
Row b: 1.5 mps
Row c: 2 mps
Row d: 2.5 mps
Row e: 3 mps

And the killer question:

Same as above, except if two or more players manage to reach the ball, they both get confused about who should catch the ball, and thus neither catch it. What is the likelihood of the ball being caught under these circumstances now?

A: You throw a coin multiple times. What's the average amount of throws required to obtain 2 heads in a row?

B: Starting at number zero, you throw a coin.
Tails means you go down one (therefore equalling -1)
Heads means you go up one (therefore equalling 1)

You repeat this procedure infinite times, so here's an example variation:
0, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 4, 5, 6, 7, 6, 7.........

Question is: (b) - how many times on average would 0 have been 'hit' if you threw the coin 100 times? The highest possible answer is 50 (0, 1, 0, 1, 0, 1 etc.), and the lowest answer is 0 (many, many ways of getting this), but I want the /average/.

I'm new here.