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Permutation question. 17 scientist vote, 4 physicicsts,7 bioligist and 6 chemist.What

  • Thread starter cloud360
  • Start date
I WANNA KNOW IF MY ANSWERS AND METHOD ARE CORRECT

1. The problem statement, all variables and given/known data

A science committee of 3 people is to be formed from a group of 17 scientists (7 biologists, 4
physicists and 6 chemists) with each possible committee equally likely.
What is the probability the committee vote in favour of a proposal given:-
(a) all biologists in favour, everybody else against?
(b) all chemists against, everybody else in favour?
(c) all biologists in favour, all chemists against and all physicists abstain?

2. Relevant equations
none


3. The attempt at a solution
Favour =Majority of comitte favour i.e at least 2 of 3 favour
For question 1
Sample space = (17C3)=680
If biologist all favour.. Then for favour, 2 biologist or 3 biologist in the comitee
Event 1= 2 biologist and 1 other=(7C2)*(10C1) =210
Event 2= 3 biologist and 0 other=(7C2)*(10C0) =35

245/Sample space = 245/680 = 49/136=36%

IS THIS CORRECT???

For question 2
Sample space = (17C3)=680

If bioligist all favour + phyicists all favour + all chemist against. Then we have many events. So is better to use addition rule.

Addition rule = E + NOT E=Sample Space..............where E= favour

NOT E= 2 chemists or 3 chemists in comitee

Event 1= 2 chemist and 1 other=(6C2)*(10C1) =150
Event 2= 3 chemist and 0 other=(6C2)*(10C0) =15

NOT E=150+15=165

(Sample space-NOT E) = E=680-165=515
515/Sample Space=Probability of E=515/680=103/136=75.7%

IS THIS CORRECT METHOD???
For question 3
Sample space = (17C3)=680

If all biologist favour + all chemist against + all physicists dont give a damn.
Favour = (3 biologist)+(2 biologist+1 Other) =Question 1
Favour = (1 bioligist + 2 physicists) +(2 bioligist + 1 physicists)
Favour = (2 bioligist + 1 chemist)

Then we have many events. So is better to use addition rule.

NOT favour=(1 chemist + 2 physicist) + (2 chemist + 1 physicist) + (3 chemist)
NOT favour=(2 chemist + bioligist)

NOT favour=(6C1)(4C2) + (6C2)(4C1) +(6C3) + (6C2)(7C1)=36+60+20+105=221

Sample space - NOT favour = 680-221=459
459/680=27/40=67.5%

IS THIS CORRECT METHOD AND ANSWER???
 
Re: Permutation question. 17 scientist vote, 4 physicicsts,7 bioligist and 6 chemist.

anyone?
 

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