Question

3.Question for further thought Imagine the two-dimensional space {0, 1, . . . , 10).(0, 1, . . . , 10) = (0,0), (0,1),(10, 10)J. We locate a mouse on the (0,0) point and we locate a piece of cheese on the (10, 10) point. We somehow make sure that the mouse will reach the cheese with 20 steps, by either going steps 'right' (for example, from (0, 0) to (0,1)) or by going steps 'up' (for example, from (0,0) to (1,0 (i) In how many ways can the mouse reach the cheese? (ii) If these ways are equally likely, what is the probability that the mouse will go all the way 'right' first (up to (0, 10)) and then all the way up'? What is the probability that the mouse will go all the way up' and then all the way 'right'? (iii) We locate two mousetraps, such that, if the mouse goes through the points (0, 10) or (10,0), wl be unable to move further. Otherwise, it will reach the cheese and then stop. Suppose that it takes exactly 5 seconds for the mouse to move from one location to the other (for example, from (i,j) to (i,j+1) or to (i+1,j. What is the expected time until the mouse will stop moving (we start counting from the beginning - at the (0,0) point) (to answer this part, consider, as in ii), that al the possible routes are equally likely)?

Answer 1