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If 20 per cent managers are technocrats, the probability that a random committee of 5 managers consists of exactly 2 technocrats is
- a)0.2048
- b)0.4000
- c)0.4096
- d)0.9421
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If 20 per cent managers are technocrats, the probability that a random...
The probability of technocrats manager = 20/100
= 1/5
∴ Probability of non technocrats manager = 4/5
Now the require probability
= 1/5
∴ Probability of non technocrats manager = 4/5
Now the require probability
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Community Answer
If 20 per cent managers are technocrats, the probability that a random...
To solve this problem, we will use the concept of probability. We are given that 20% of the managers are technocrats. Let's break down the problem step by step:
Step 1: Calculate the probability of selecting a technocrat
Since 20% of the managers are technocrats, the probability of selecting a technocrat is 0.20.
Step 2: Calculate the probability of selecting a non-technocrat
The remaining managers who are not technocrats would be 80%. Therefore, the probability of selecting a non-technocrat is 0.80.
Step 3: Calculate the probability of selecting exactly 2 technocrats in a committee of 5 managers
To calculate this probability, we need to use the concept of combinations. The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items to be selected, and the exclamation mark represents factorial.
In this case, there are 5 managers in the committee, and we want to select exactly 2 technocrats. Therefore, n = 5 and r = 2.
The number of ways to select exactly 2 technocrats from 5 managers can be calculated as follows:
5C2 = 5! / (2!(5-2)!) = 5! / (2!3!) = (5 * 4) / (2 * 1) = 10
Step 4: Calculate the probability of selecting exactly 2 technocrats
Now, we need to multiply the probability of selecting a technocrat (0.20) by the probability of selecting a non-technocrat (0.80) and the number of ways to select exactly 2 technocrats (10).
Probability = (0.20)^2 * (0.80)^3 * 10 = 0.008 * 0.512 * 10 = 0.04096
Therefore, the probability that a random committee of 5 managers consists of exactly 2 technocrats is 0.04096 or 0.4096.
However, in the given options, none of them matches the calculated probability. Therefore, the correct answer is not provided in the options given.
Step 1: Calculate the probability of selecting a technocrat
Since 20% of the managers are technocrats, the probability of selecting a technocrat is 0.20.
Step 2: Calculate the probability of selecting a non-technocrat
The remaining managers who are not technocrats would be 80%. Therefore, the probability of selecting a non-technocrat is 0.80.
Step 3: Calculate the probability of selecting exactly 2 technocrats in a committee of 5 managers
To calculate this probability, we need to use the concept of combinations. The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items to be selected, and the exclamation mark represents factorial.
In this case, there are 5 managers in the committee, and we want to select exactly 2 technocrats. Therefore, n = 5 and r = 2.
The number of ways to select exactly 2 technocrats from 5 managers can be calculated as follows:
5C2 = 5! / (2!(5-2)!) = 5! / (2!3!) = (5 * 4) / (2 * 1) = 10
Step 4: Calculate the probability of selecting exactly 2 technocrats
Now, we need to multiply the probability of selecting a technocrat (0.20) by the probability of selecting a non-technocrat (0.80) and the number of ways to select exactly 2 technocrats (10).
Probability = (0.20)^2 * (0.80)^3 * 10 = 0.008 * 0.512 * 10 = 0.04096
Therefore, the probability that a random committee of 5 managers consists of exactly 2 technocrats is 0.04096 or 0.4096.
However, in the given options, none of them matches the calculated probability. Therefore, the correct answer is not provided in the options given.
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If 20 per cent managers are technocrats, the probability that a random committee of 5 managers consists of exactly 2 technocrats isa)0.2048 b)0.4000 c)0.4096 d)0.9421Correct answer is option 'A'. Can you explain this answer?
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If 20 per cent managers are technocrats, the probability that a random committee of 5 managers consists of exactly 2 technocrats isa)0.2048 b)0.4000 c)0.4096 d)0.9421Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If 20 per cent managers are technocrats, the probability that a random committee of 5 managers consists of exactly 2 technocrats isa)0.2048 b)0.4000 c)0.4096 d)0.9421Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 20 per cent managers are technocrats, the probability that a random committee of 5 managers consists of exactly 2 technocrats isa)0.2048 b)0.4000 c)0.4096 d)0.9421Correct answer is option 'A'. Can you explain this answer?.
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