Assume the probability of certain material to be detective produced by a company is 0.1 to inspect 10 items are selected so, probability at least one is defective
To calculate the probability that at least one item is defective, we can use the concept of complementary probability. This means finding the probability that no items are defective and subtracting it from 1.
The probability that no items are defective can be calculated by taking the probability that one item is not defective and raising it to the power of the number of items selected.
In this case, the probability that one item is not defective is 1 minus the probability that it is defective. Given that the probability of an item being defective is 0.1, the probability that it is not defective is 1 - 0.1 = 0.9.
So, the probability that no items are defective out of 10 selected items is (0.9)^10.
Therefore, the probability that at least one item is defective is 1 - (0.9)^10.
Let's calculate it:
Probability of at least one defective item = 1 - (0.9)^10
Probability of at least one defective item = 1 - 0.3487
Therefore, the probability of at least one defective item is approximately 0.6513 or 65.13%.