Lunches for three brothers Adam, Ben, and Carl are made and the lunch bags are marked with their names. It's dark when they leave for school. They each pick up a lunch bag as they go out the door. What is the probability that no one gets their own lunch?
2006-10-11 12:43:47 · 8 answers · asked by aguila09@sbcglobal.net 1 in Science & Mathematics ➔ Mathematics
Just assume that Adam takes the first lunch, Ben the second and Carl the third, but they could randomly be in any order.
There are six arrangements:
ABC (Adam, Ben and Carl get their same lunch)
ACB (Adam gets his lunch)
BAC (Carl gets his lunch)
BCA <-- none match
CAB <-- none match
CBA (Ben gets his lunch)
Of these only two have the bags completely out of order (none match), so the answer is 2/6 which reduces to 1/3.
The probability is therefore 1/3 that *no one* gets their own lunch.
2006-10-11 12:50:38 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
1 to 3
2006-10-11 19:47:05 · answer #2 · answered by ♥_mrs.smith 4 · 0⤊ 0⤋
There are 3! = 6 ways for the three boys to get the lunches. Assume that CBA means that Adam gets Carl's lunch, Ben gets
Ben's lunch, and Carl get's Adams lunch.
ABC (Meaning A gets A, B gets B, C gets C)
ACB (Meaning A gets A, B gets C, C gets B)
BAC (Meaning A gets B, B gets A, C gets C)
BCA (Meaning A gets B, B gets C, C gets A)
CAB (Meaning A gets C, B gets A, C gets B)
CBA (Meaning A gets C, B gets B, C gets A)
Of these six, 2 result in none of the boys getting their own lunch, so 2/6 or 1/3.
2006-10-11 19:51:21 · answer #3 · answered by blahb31 6 · 0⤊ 0⤋
1:3
2006-10-11 19:46:29 · answer #4 · answered by beeboroachgoingon197 1 · 0⤊ 0⤋
One out of 3.
2006-10-11 19:52:00 · answer #5 · answered by Bluealt 7 · 0⤊ 0⤋
(2/3)*(1/2)*(1) = 1/3
2006-10-11 19:48:50 · answer #6 · answered by Steve 7 · 0⤊ 0⤋
If there are n brothers, this can be calculated as
1/2! -1/3! +1/4! -1/5! +.....(-1)^n/n!
As n increases to infinity, the odds approach
e^(-1) or approx 0.367879441
2006-10-11 20:10:14 · answer #7 · answered by PC_Load_Letter 4 · 0⤊ 0⤋
9
multiply 3(brothers) by 3(lunches)
2006-10-11 19:46:14 · answer #8 · answered by Make Love Not War! 4 · 0⤊ 0⤋