Hello! I am having a problem with knowing the number of ways a boy can walk to be at a certain position in the following exercise ,I would very much appreciate some help.
"A boy stands on a street corner and tosses a fair die .If 1 or 2 occurs, he walks one block west ;otherwise he walks one block east. At his new position he repeats the procedure. What is the probability that after having tossed the coin 6 times he is
(a) at his starting point;
(b)2 blocks from his starting point;
(c)4 blocks from his starting point."
Now i realize that the probability of the boy walking west is 2/6=1/3 and of him walking east is 4/6=2/3.
Being at his starting point means that at the end he would have walked 3 blocks west and 3 blocks east meaning that the probability is (1/3)^3*(2/3)^3 ,but there are plenty of ways he could have walked these 6 blocks ,I am having trouble knowing the number of ways he could have walked these blocks .
For the second question -being 2 blocks from the starting point -means that he could either be 2 blocks west or two blocks east which have different probabilities in this case .
Overall I am wondering if there is an easier approach to solve these kind of problems or maybe a generic way to find out how to calculate these probabilities let's say if he tossed the coin n times.
"A boy stands on a street corner and tosses a fair die .If 1 or 2 occurs, he walks one block west ;otherwise he walks one block east. At his new position he repeats the procedure. What is the probability that after having tossed the coin 6 times he is
(a) at his starting point;
(b)2 blocks from his starting point;
(c)4 blocks from his starting point."
Now i realize that the probability of the boy walking west is 2/6=1/3 and of him walking east is 4/6=2/3.
Being at his starting point means that at the end he would have walked 3 blocks west and 3 blocks east meaning that the probability is (1/3)^3*(2/3)^3 ,but there are plenty of ways he could have walked these 6 blocks ,I am having trouble knowing the number of ways he could have walked these blocks .
For the second question -being 2 blocks from the starting point -means that he could either be 2 blocks west or two blocks east which have different probabilities in this case .
Overall I am wondering if there is an easier approach to solve these kind of problems or maybe a generic way to find out how to calculate these probabilities let's say if he tossed the coin n times.