Question 433456: I cant finish these homework problems. The problem is set up as a rectangle with 6 columns down and 3 rows across. a is in the left corner and z is in the bottom right. b is located 2 columns across starting at a, one row down. C is located 3 columns across ad 2 rows down from a.
a[][][][][][]
[][]b[][][][]
[][][]c[][][]z
) Given that a route passes through B, what is the probability that it also passes through point C? Answer in fraction.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I cant finish these homework problems. The problem is set up as a rectangle with 6 columns down and 3 rows across. a is in the left corner and z is in the bottom right. b is located 2 columns across starting at a, one row down. C is located 3 columns across ad 2 rows down from a.
a[][][][][][]
[][]b[][][][]
[][][]c[][][]z
2. (1 point) If a route (with no backtracking) from A to Z is randomly chosen, what is the probability that the route passes through point B? Answer in fraction.----
# of routes from a to z: 2*3*4*5*6*5*4*3*2*1 = 6!*5! = 86400
# of rountes from a to z thru b: 2*1*4*5*6*5*4*3*2*1 = 28800
P(a to z thru b) = 1/3
Note: I'm assuming the "b" box is to the left of your letter "b".
If it's to the right the answer is 1/4
--------------------------------------------
3. (1 point) Given that a route passes through B, what is the probability that it also passes through point C? Answer in fraction.
----
I'll leave the counting to you:
P(B|C| = P(B and C)/P(C)
=============================
Cheers,
Stan H.
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Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
The other tutor's answer is incorrect.
I will assume that by "path" you mean that you always start from a,
then move right or down, never left or up.
[ a ][ ][ ][ ][ ][ ][ ]
[ ][ ][ b ][ ][ ][ ][ ]
[ ][ ][ ][ c ][ ][ ][ z ]
I will indicate with a right arrow → that the next move from
that space will be to the right, and indicate with a down arrow ↓
that the next move will be downward.
There are only three ways to go from a to b:
#1.
[ a→][ →][ ↓ ][ ][ ][ ][ ]
[ ][ ][ b ][ ][ ][ ][ ]
[ ][ ][ ][ c ][ ][ ][ z ]
#2.
[ a→][ ↓ ][ ][ ][ ][ ][ ]
[ ][ →][ b ][ ][ ][ ][ ]
[ ][ ][ ][ c ][ ][ ][ z ]
#3.
[ a↓][ ][ ][ ][ ][ ][ ]
[ →][ →][ b ][ ][ ][ ][ ]
[ ][ ][ ][ c ][ ][ ][ z ]
But that's irrelevant, because you are given that your path goes
through b. Therefore regardless of how you got from a to b, there
are only these 5 ways to get from b to z, 2 go through c and 3
don't.
1.
[ a ][ ][ ][ ][ ][ ][ ]
[ ][ ][ b→][ →][ →][ →][ ↓ ]
[ ][ ][ ][ c ][ ][ ][ z ] Does not go through c
2.
[ a ][ ][ ][ ][ ][ ][ ]
[ ][ ][ b→][ →][ →][ ↓ ][ ]
[ ][ ][ ][ c ][ ][ →][ z ] Does not go through c
3.
[ a ][ ][ ][ ][ ][ ][ ]
[ ][ ][ b→][ →][ ↓ ][ ][ ]
[ ][ ][ ][ c ][ →][ →][ z ] Does not go through c
4.
[ a ][ ][ ][ ][ ][ ][ ]
[ ][ ][ b→][ ↓ ][ ][ ][ ]
[ ][ ][ ][ c→][ →][ →][ z ] Goes through c
5.
[ a ][ ][ ][ ][ ][ ][ ]
[ ][ ][ b↓][ ][ ][ ][ ]
[ ][ ][ →][ c→][ →][ →][z ] Goes through c
Therefore the probability of going from b through c from b
is 2 ways out of 5, or a probability of 2/5
Edwin
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