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A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctor
a) what is the probability that each of the four professions is represented on the committee?
b) what is the probability that the committee consist of the doctor and at least one economist?
a) what is the probability that each of the four professions is represented on the committee?
b) what is the probability that the committee consist of the doctor and at least one economist?
Most Upvoted Answer
A committee of four has been formed from among 3 economist, 4 engineer...
Probability of each profession being represented on the committee:
- Total number of ways to choose 4 members from 10 individuals: ${10 \choose 4} = 210$
- Number of ways to choose 1 economist, 1 engineer, 1 statistician, and 1 doctor: $3 \times 4 \times 2 \times 1 = 24$
- Probability that each profession is represented: $\frac{24}{210} = \frac{4}{35}$
Probability of the committee consisting of the doctor and at least one economist:
- Total number of ways to choose 4 members from 10 individuals: ${10 \choose 4} = 210$
- Number of ways to choose the doctor and at least one economist: $1 \times {3 \choose 1} \times {6 \choose 2} = 45$
- Probability of the committee consisting of the doctor and at least one economist: $\frac{45}{210} = \frac{3}{14}$
Therefore, the probability that each profession is represented on the committee is $\frac{4}{35}$ and the probability that the committee consists of the doctor and at least one economist is $\frac{3}{14}$.
- Total number of ways to choose 4 members from 10 individuals: ${10 \choose 4} = 210$
- Number of ways to choose 1 economist, 1 engineer, 1 statistician, and 1 doctor: $3 \times 4 \times 2 \times 1 = 24$
- Probability that each profession is represented: $\frac{24}{210} = \frac{4}{35}$
Probability of the committee consisting of the doctor and at least one economist:
- Total number of ways to choose 4 members from 10 individuals: ${10 \choose 4} = 210$
- Number of ways to choose the doctor and at least one economist: $1 \times {3 \choose 1} \times {6 \choose 2} = 45$
- Probability of the committee consisting of the doctor and at least one economist: $\frac{45}{210} = \frac{3}{14}$
Therefore, the probability that each profession is represented on the committee is $\frac{4}{35}$ and the probability that the committee consists of the doctor and at least one economist is $\frac{3}{14}$.
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A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist?
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A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist?.
A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of four has been formed from among 3 economist, 4 engineers, 2 statisticians, and 1 doctora) what is the probability that each of the four professions is represented on the committee?b) what is the probability that the committee consist of the doctor and at least one economist?.
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