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Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, is
- a)70.65%
- b)71.65%
- c)74.65%
- d)72.65%
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Three screws are drawn at random from a lot of 100 screws, 10 of whic...
The probability of the event that all 3 screws drawn are non-defective =
(90/100) x (89/99) x (88/98) = 72.65%
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Community Answer
Three screws are drawn at random from a lot of 100 screws, 10 of whic...
To find the probability that all 3 screws drawn are non-defective, we need to find the ratio of the number of favorable outcomes (i.e., when all 3 screws are non-defective) to the total number of possible outcomes.
Total number of screws = 100
Number of defective screws = 10
Step 1: Finding the probability of selecting the first non-defective screw
When the first screw is drawn, there are 100 screws in total, out of which 10 are defective. Therefore, the probability of selecting a non-defective screw at the first draw is:
P(First non-defective screw) = (100 - 10) / 100 = 90 / 100 = 9 / 10
Step 2: Finding the probability of selecting the second non-defective screw
After the first non-defective screw is drawn, there are 99 screws left, out of which 9 are non-defective. Therefore, the probability of selecting a non-defective screw at the second draw is:
P(Second non-defective screw) = (99 - 9) / 99 = 90 / 99
Step 3: Finding the probability of selecting the third non-defective screw
After the second non-defective screw is drawn, there are 98 screws left, out of which 8 are non-defective. Therefore, the probability of selecting a non-defective screw at the third draw is:
P(Third non-defective screw) = (98 - 8) / 98 = 90 / 98 = 45 / 49
Step 4: Finding the probability of all 3 screws being non-defective
Since the screws are drawn without replacement, the probabilities calculated in steps 1, 2, and 3 are multiplied together to find the probability of all 3 screws being non-defective:
P(All 3 screws non-defective) = P(First non-defective screw) * P(Second non-defective screw) * P(Third non-defective screw)
= (9/10) * (90/99) * (45/49)
= 0.9 * 0.9091 * 0.9184
≈ 0.7465
Therefore, the probability of all 3 screws drawn being non-defective is approximately 74.65%, which corresponds to option (d).
Total number of screws = 100
Number of defective screws = 10
Step 1: Finding the probability of selecting the first non-defective screw
When the first screw is drawn, there are 100 screws in total, out of which 10 are defective. Therefore, the probability of selecting a non-defective screw at the first draw is:
P(First non-defective screw) = (100 - 10) / 100 = 90 / 100 = 9 / 10
Step 2: Finding the probability of selecting the second non-defective screw
After the first non-defective screw is drawn, there are 99 screws left, out of which 9 are non-defective. Therefore, the probability of selecting a non-defective screw at the second draw is:
P(Second non-defective screw) = (99 - 9) / 99 = 90 / 99
Step 3: Finding the probability of selecting the third non-defective screw
After the second non-defective screw is drawn, there are 98 screws left, out of which 8 are non-defective. Therefore, the probability of selecting a non-defective screw at the third draw is:
P(Third non-defective screw) = (98 - 8) / 98 = 90 / 98 = 45 / 49
Step 4: Finding the probability of all 3 screws being non-defective
Since the screws are drawn without replacement, the probabilities calculated in steps 1, 2, and 3 are multiplied together to find the probability of all 3 screws being non-defective:
P(All 3 screws non-defective) = P(First non-defective screw) * P(Second non-defective screw) * P(Third non-defective screw)
= (9/10) * (90/99) * (45/49)
= 0.9 * 0.9091 * 0.9184
≈ 0.7465
Therefore, the probability of all 3 screws drawn being non-defective is approximately 74.65%, which corresponds to option (d).
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Three screws are drawn at random from a lot of 100 screws, 10 of which are defective. The probability of the event that all 3 screws drawn are non-defective, assuming that the screws are drawn without replacement, isa)70.65%b)71.65%c)74.65%d)72.65%Correct answer is option 'D'. Can you explain this answer?
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