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There are 100 screws in a box out of which 10 are defective, three of these screws are lifted randomly, what is the probability that the three screws are not defective?

There are 100 screws in a box out of which 10 are defective, three of these screws are lifted randomly, what is the probability that the three screws are not defective? Correct Answer 72.65%

Given:

Total screws = 100

Defective = 10

Concept used:

nCr = n!/

Where, n = The number of items, r = How many items are taken at a time.

Probability (E) = (Number of favorable outcomes)/(Total no. of possible outcomes)

Calculation:

Total number of outcomes to select three screws = 100C3 

Number of non defective screws = 100 – 10 = 90

Total number of ways to select three non-defective screws = 90C3

Probability of getting a non-defective screw = (90C3)/(100C3)

⇒ Probability of getting a non-defective screw = (90 × 89 × 88)/(100 × 99 × 98)

⇒ Probability of getting a non-defective screw ≈ 0.7265

Converting the decimal into percentage we'll get 0.7265 × 100 = 72.65%

∴ Probability that the three screws are not defective is 72.65%

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