Check Your Answers: Probability of a Committee Vote Favour

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In summary, the conversation discusses the probability of a committee formed from a group of 17 scientists voting in favor of a proposal, given different scenarios. The first scenario looks at the probability if all biologists are in favor and everyone else is against, with a probability of 36%. The second scenario examines the probability if all chemists are against and everyone else is in favor, with a probability of 75.7%. The final scenario looks at the probability if all biologists are in favor, all chemists are against, and all physicists abstain, with a probability of 67.5%. The methods used for calculating these probabilities involved using the addition rule and the formula for combinations.
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cloud360
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I WANNA KNOW IF MY ANSWERS AND METHOD ARE CORRECT

Homework Statement



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?

Homework Equations


none


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 don't 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?
 
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anyone?
 

1. What is the purpose of checking the probability of a committee vote favor?

The purpose of checking the probability of a committee vote favor is to determine the likelihood of a particular outcome, in this case, a favorable vote from the committee. This can help in decision-making and planning for potential scenarios.

2. How is the probability of a committee vote favor calculated?

The probability of a committee vote favor is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if there are 10 members on the committee and 6 of them are expected to vote favorably, the probability would be 6/10 or 60%.

3. Can the probability of a committee vote favor change?

Yes, the probability of a committee vote favor can change based on various factors such as new information, changes in opinions, or external influences. It is important to regularly reassess the probability to make informed decisions.

4. How can I increase the probability of a committee vote favor?

There are a few ways to increase the probability of a committee vote favor. These include building relationships with committee members, presenting a strong and convincing argument, and addressing any concerns or objections they may have. It is also important to understand the dynamics of the committee and tailor your approach accordingly.

5. Is the probability of a committee vote favor always accurate?

No, the probability of a committee vote favor is not always accurate. It is based on assumptions and predictions and can be influenced by various factors. It is important to consider all possible outcomes and not rely solely on the calculated probability.

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