SOLUTION: 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 locate

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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.
=============
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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