Question

An ant starts from the original of a 2-D grid, at the point (0,0). Then each time it moves either

i) right by one unit distance, e.g., from (0,0) to (1,0),

ii) up by one unit distance, e.g., from (0,0) to (0,1), or

iii) stay still with probabilities 0.3, 0.2, and 0.5, respectively.

After 10 moves, what is the probability that the ant settles down at point (2,5)?

Answer 1

For the ant to settle down at point (2,5) after 10 moves its should have moved 2 units right, 5 units up and 3 times stay still.

The respective probabilities are 0.3, 0.2, and 0.5. Out of 10, 2 are right moves, 5 are up moves and 3 remains still. The probability the ant settles down at the point (2,5) is the multinomial probability,