pranab223 wrote:
sandy wrote:
Six people are asked to sit down in a circle consisting of eight chairs.Assume that the six people are in fact three couples.What is the probability that at least one of the three wives will sit next to her husband if everybody takes a seat randomly.
P = 6/7
Number of arrangements where at least one wife sits next to her husband:
Using complement rule
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(at least 1 matching couple) = 1 - P(zero matching couple)
P(zero matching couple) =6/8 x 4/7 x 2/6
= 1/7
So, P(at least 1 couple) = 1 - P(no couple)
= 1 - 1/7
= 6/7
Hi, Thank you for explanation, I am trying to understand how your equation meets which use cases.
It does not change conclusion, but, should' P(zero matching couple) be, = 5/7 x 3/5 x 1/3 = 1/7 ?
#1st couple, (F1,F2)
F1 seat can be anything from 8 empty seats.
Remaining 7 (8-1) seats. (?/7)
F2 cannot be next to F1, so need to be picked from 5 seats (7-2)
5/7
#2nd couple, (S1,S2)
S1 seat can be anything from remaining 6 seats. (6 = (8-2) as 2 seats are taken by F1,F2)
Remaining 5(6-1) seats. (?/5)
S2 cannot be next to S1, so need to be picked from 3 seats (5-2)
3/5
#3rd couple (T1, T2)
T1 seat can be anything from remaining 4 seats. (4 = (8-4) as 4 seats are taken by F1,F2, S2,S2)
Remaining 3 (4-1) seats (?/3)
T2 cannot be next to T1,so need to be picked from 1 seats (3-2)
1/3
5/7 * 3/5 * 1/3 = 1/7
I am trying to understand whether above equation means same concept which you explained.
Thank you in advance.