A total of 10 people, consisting of 5 married couples, are randomley seated in a row for a photo.
Let Ci denote the event that the ith couple are seated next to each other, i=1....5, and X be the
total number of couples that are seated next to each other.
a) find P(Ci) (i know this is 2/10)
b) for j not eqaul to I, find the cond. probability that P(Cj/Ci)
c) Find the expeted value for E[x] and var(X) of X.
Thank you, DETAILED EXPLANATION!
Solution
a) P(Ci)
we can consider ith couple as one unit and other 8 persons as individuals.
Thus, no. of arrangements = 2 * 9!
Total no. of possible arrangements = 10!
Thus, P(Ci) = 2 * 9! / 10! = 2/10 = 1/5
b) P(Cj|Ci)
Now, we have Ci as a couple, Cj as a couple
No. of possible cases = 2 * 2 * 8! = 4 * 8!
Total possible cases = 2 * 9!
Thus, P(Cj|Ci) = 4 * 8! / 2 * 9! = 2/9.
A total of 10 people, consisting of 5 married couples, are randomley.pdf
1. A total of 10 people, consisting of 5 married couples, are randomley seated in a row for a photo.
Let Ci denote the event that the ith couple are seated next to each other, i=1....5, and X be the
total number of couples that are seated next to each other.
a) find P(Ci) (i know this is 2/10)
b) for j not eqaul to I, find the cond. probability that P(Cj/Ci)
c) Find the expeted value for E[x] and var(X) of X.
Thank you, DETAILED EXPLANATION!
Solution
a) P(Ci)
we can consider ith couple as one unit and other 8 persons as individuals.
Thus, no. of arrangements = 2 * 9!
Total no. of possible arrangements = 10!
Thus, P(Ci) = 2 * 9! / 10! = 2/10 = 1/5
b) P(Cj|Ci)
Now, we have Ci as a couple, Cj as a couple
No. of possible cases = 2 * 2 * 8! = 4 * 8!
Total possible cases = 2 * 9!
Thus, P(Cj|Ci) = 4 * 8! / 2 * 9! = 2/9
![A total of 10 people, consisting of 5 married couples, are randomley seated in a row for a photo.
Let Ci denote the event that the ith couple are seated next to each other, i=1....5, and X be the
total number of couples that are seated next to each other.
a) find P(Ci) (i know this is 2/10)
b) for j not eqaul to I, find the cond. probability that P(Cj/Ci)
c) Find the expeted value for E[x] and var(X) of X.
Thank you, DETAILED EXPLANATION!
Solution
a) P(Ci)
we can consider ith couple as one unit and other 8 persons as individuals.
Thus, no. of arrangements = 2 * 9!
Total no. of possible arrangements = 10!
Thus, P(Ci) = 2 * 9! / 10! = 2/10 = 1/5
b) P(Cj|Ci)
Now, we have Ci as a couple, Cj as a couple
No. of possible cases = 2 * 2 * 8! = 4 * 8!
Total possible cases = 2 * 9!
Thus, P(Cj|Ci) = 4 * 8! / 2 * 9! = 2/9](https://image.slidesharecdn.com/atotalof10peopleconsistingof5marriedcouplesarerandomley-230324035146-b89e34c9/85/A-total-of-10-people-consisting-of-5-married-couples-are-randomley-pdf-1-320.jpg)
