Question 1192736: In tossing a pair of dice and a pair of coins simultaneously, what is the probability of getting a sum of 6, a tail, and a head?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
Lets look at the dice first: There are 36 possible outcomes, of these we have this table for the sums:
Sum # ways
2 1
3 2
4 3
5 4
6 5 (1+5, 2+4, 3+3, 4+2, 5+1, where we consider first die + second die)
7 6
8 5
9 4
10 3
11 2
12 1
----
36
So a sum of 6 will have probability 5/36 (this should make sense!)
Now look at the two coin flips:
HH
HT
TH
TT
A head and tail can be tossed with probability 2/4 = 1/2
Since these events are independent, we multiply: (5/36)*(1/2) = 
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
In this problem, as it is worded, it is unclear, if the tail and head considered as produced by two coins
in this special / specific order OR the order of H and T does not matter.
The answer is different in these different cases.
So, when the problem goes without specifying whether the order does matter,
then the problem is ambiguous and, THEREFORE, is DEFECTIVE.
A ticket to the problem's composer for his (or her) careless job.
|
|
|
