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A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from the packet at random, what is the expected value of the number of defective?
- a)1.20
- b)1.21
- c)1.69
- d)1.72
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A packet of 10 electronic components is known to include 3 defectives....
Given:
- A packet of 10 electronic components
- 3 of them are defectives
- 4 components are selected at random
To find: Expected value of the number of defective components
Approach:
- We can use the formula of expected value to solve this problem.
- Expected value = Sum of (each possible value * probability of that value)
Calculation:
- There can be 0, 1, 2, 3 or 4 defective components in the selected 4 components.
- Let's calculate the probability of each possible value.
Probability of 0 defective components:
- We need to select 4 components out of 7 non-defective components.
- Number of ways = C(7,4) = 35
- Total number of ways to select 4 components out of 10 = C(10,4) = 210
- Probability = 35/210 = 1/6
Probability of 1 defective component:
- We need to select 1 defective component and 3 non-defective components.
- Number of ways = C(3,1) * C(7,3) = 3 * 35 = 105
- Probability = 105/210 = 1/2
Probability of 2 defective components:
- We need to select 2 defective components and 2 non-defective components.
- Number of ways = C(3,2) * C(7,2) = 3 * 21 = 63
- Probability = 63/210 = 3/10
Probability of 3 defective components:
- We need to select 3 defective components and 1 non-defective component.
- Number of ways = C(3,3) * C(7,1) = 1 * 7 = 7
- Probability = 7/210 = 1/30
Probability of 4 defective components:
- We need to select 4 defective components.
- Number of ways = C(3,4) = 0
- Probability = 0/210 = 0
Expected value:
- Expected value = Sum of (each possible value * probability of that value)
- Expected value = 0 * (1/6) + 1 * (1/2) + 2 * (3/10) + 3 * (1/30) + 4 * 0
- Expected value = 1.2
Therefore, the expected value of the number of defective components is 1.20.
Hence, option (a) is the correct answer.
- A packet of 10 electronic components
- 3 of them are defectives
- 4 components are selected at random
To find: Expected value of the number of defective components
Approach:
- We can use the formula of expected value to solve this problem.
- Expected value = Sum of (each possible value * probability of that value)
Calculation:
- There can be 0, 1, 2, 3 or 4 defective components in the selected 4 components.
- Let's calculate the probability of each possible value.
Probability of 0 defective components:
- We need to select 4 components out of 7 non-defective components.
- Number of ways = C(7,4) = 35
- Total number of ways to select 4 components out of 10 = C(10,4) = 210
- Probability = 35/210 = 1/6
Probability of 1 defective component:
- We need to select 1 defective component and 3 non-defective components.
- Number of ways = C(3,1) * C(7,3) = 3 * 35 = 105
- Probability = 105/210 = 1/2
Probability of 2 defective components:
- We need to select 2 defective components and 2 non-defective components.
- Number of ways = C(3,2) * C(7,2) = 3 * 21 = 63
- Probability = 63/210 = 3/10
Probability of 3 defective components:
- We need to select 3 defective components and 1 non-defective component.
- Number of ways = C(3,3) * C(7,1) = 1 * 7 = 7
- Probability = 7/210 = 1/30
Probability of 4 defective components:
- We need to select 4 defective components.
- Number of ways = C(3,4) = 0
- Probability = 0/210 = 0
Expected value:
- Expected value = Sum of (each possible value * probability of that value)
- Expected value = 0 * (1/6) + 1 * (1/2) + 2 * (3/10) + 3 * (1/30) + 4 * 0
- Expected value = 1.2
Therefore, the expected value of the number of defective components is 1.20.
Hence, option (a) is the correct answer.
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Community Answer
A packet of 10 electronic components is known to include 3 defectives....
Average Defective Components = 3/10
So, Expected Value of Defective in 4 = 3/10*4=1.2
So, Expected Value of Defective in 4 = 3/10*4=1.2
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A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from the packet at random, what is the expected value of the number of defective?a)1.20b)1.21c)1.69d)1.72Correct answer is option 'A'. Can you explain this answer?
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