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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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