There are 9 boys and 7 girls sitting around a

wanaopatays

wanaopatays

Answered question

2022-05-28

There are 9 boys and 7 girls sitting around a table. If a boy sits next to a girl we call it a switch. Example: In BBBBBGGGBBGBGGG there are 6 switches.(If a boy sits next to 2 girls, there are 2 switches counted.) What is the expected number of switches?

Answer & Explanation

vikafa4g

vikafa4g

Beginner2022-05-29Added 15 answers

Give the boys a number. For boy i let G i denote the number of girls that sit next to him.
Then you are searching for:
E ( G 1 + + G 9 ) = E G 1 + + E G 9 = 9 E G 1
Let Alex (the boy having number 1) take place.
The probability that Alex will get 2 boys as neighbor is 8 15 7 14 = 4 15 .
The probability that Alex will get 2 girls as neighbor is 7 15 6 14 = 3 15
The probability that Alex will get a girl and a boy as neighbor is 2 8 15 7 14 = 8 15
So E G 1 = 0 × 4 15 + 2 × 3 15 + 1 × 8 15 = 14 15
We come to an expectation of 9 × 14 15 = 42 5 switches.
Trevor Wood

Trevor Wood

Beginner2022-05-30Added 5 answers

Let X i { 0 , 1 , 2 } be the count of switches next to boy i.
Then the expected number of switches is: E ( i = 1 9 X i )

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