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A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective?
- a)1/5
- b)1/25
- c)20/99
- d)11/495
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A box contains 20 defective items and 80 non-defective items. If two i...
Total number of items = 100
Number of defective items = 20
Number of Non-defective items = 80
Then the probability that both items are defective, when 2 items are selected at random is,
⇒ P= (20C2x80C0)/(100C2) = 19/495
Most Upvoted Answer
A box contains 20 defective items and 80 non-defective items. If two i...
To solve this problem, we can use the concept of probability.
Let's break down the problem into steps:
Step 1: Determine the total number of items in the box
The box contains 20 defective items and 80 non-defective items, so the total number of items in the box is 20 + 80 = 100.
Step 2: Determine the probability of selecting the first defective item
Since there are 20 defective items out of 100 total items, the probability of selecting a defective item on the first draw is 20/100 = 1/5.
Step 3: Determine the probability of selecting a second defective item, given that the first item was defective
After the first defective item is selected, there are now 19 defective items left in the box, out of a total of 99 items (since one item has already been drawn). Therefore, the probability of selecting a second defective item, given that the first item was defective, is 19/99.
Step 4: Determine the probability of both items being defective
To find the probability of both items being defective, we need to multiply the probability of selecting the first defective item (1/5) by the probability of selecting a second defective item, given that the first item was defective (19/99).
Probability = (1/5) * (19/99) = 19/495
Therefore, the correct answer is option D) 19/495.
Let's break down the problem into steps:
Step 1: Determine the total number of items in the box
The box contains 20 defective items and 80 non-defective items, so the total number of items in the box is 20 + 80 = 100.
Step 2: Determine the probability of selecting the first defective item
Since there are 20 defective items out of 100 total items, the probability of selecting a defective item on the first draw is 20/100 = 1/5.
Step 3: Determine the probability of selecting a second defective item, given that the first item was defective
After the first defective item is selected, there are now 19 defective items left in the box, out of a total of 99 items (since one item has already been drawn). Therefore, the probability of selecting a second defective item, given that the first item was defective, is 19/99.
Step 4: Determine the probability of both items being defective
To find the probability of both items being defective, we need to multiply the probability of selecting the first defective item (1/5) by the probability of selecting a second defective item, given that the first item was defective (19/99).
Probability = (1/5) * (19/99) = 19/495
Therefore, the correct answer is option D) 19/495.
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A box contains 20 defective items and 80 non-defective items. If two i...
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A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective? a)1/5 b)1/25 c)20/99 d)11/495Correct answer is option 'D'. Can you explain this answer?
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