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What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item?
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What is the chance of getting at least one defective item if 3 items a...
Calculating the Probability of Getting at Least One Defective Item
To calculate the probability of getting at least one defective item when drawing 3 items randomly from a lot containing 6 items (2 of which are defective), we need to consider the different scenarios that satisfy this condition.
Determine the Total Number of Ways to Draw 3 Items from a Lot of 6
- The total number of ways to draw 3 items from a lot of 6 can be calculated using the combination formula: C(n, r) = n! / [r!(n-r)!]
- In this case, C(6, 3) = 6! / [3!(6-3)!] = 20
Determine the Number of Ways to Draw 3 Non-Defective Items
- To calculate the number of ways to draw 3 non-defective items, we need to consider drawing all 3 items from the 4 non-defective items in the lot.
- C(4, 3) = 4! / [3!(4-3)!] = 4
Calculate the Probability of Drawing 3 Non-Defective Items
- The probability of drawing 3 non-defective items is given by the number of favorable outcomes divided by the total number of outcomes: P(3 non-defective items) = 4/20 = 0.2
Calculate the Probability of Drawing at Least One Defective Item
- The probability of drawing at least one defective item is the complement of drawing 3 non-defective items: P(at least one defective item) = 1 - P(3 non-defective items) = 1 - 0.2 = 0.8
Therefore, the chance of getting at least one defective item when drawing 3 items randomly from a lot containing 6 items (2 of which are defective) is 0.8 or 80%.
To calculate the probability of getting at least one defective item when drawing 3 items randomly from a lot containing 6 items (2 of which are defective), we need to consider the different scenarios that satisfy this condition.
Determine the Total Number of Ways to Draw 3 Items from a Lot of 6
- The total number of ways to draw 3 items from a lot of 6 can be calculated using the combination formula: C(n, r) = n! / [r!(n-r)!]
- In this case, C(6, 3) = 6! / [3!(6-3)!] = 20
Determine the Number of Ways to Draw 3 Non-Defective Items
- To calculate the number of ways to draw 3 non-defective items, we need to consider drawing all 3 items from the 4 non-defective items in the lot.
- C(4, 3) = 4! / [3!(4-3)!] = 4
Calculate the Probability of Drawing 3 Non-Defective Items
- The probability of drawing 3 non-defective items is given by the number of favorable outcomes divided by the total number of outcomes: P(3 non-defective items) = 4/20 = 0.2
Calculate the Probability of Drawing at Least One Defective Item
- The probability of drawing at least one defective item is the complement of drawing 3 non-defective items: P(at least one defective item) = 1 - P(3 non-defective items) = 1 - 0.2 = 0.8
Therefore, the chance of getting at least one defective item when drawing 3 items randomly from a lot containing 6 items (2 of which are defective) is 0.8 or 80%.
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What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item?
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What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item?.
What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item?.
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