Question

items produced by a certain company are subjected to two kind of defected D1 and D2. out of the total product 5% have the defect D1, 10% have the defect D2 and 2% have both defects. what is probablity that a randomly selected item has neither D1 or D2?

Answer 1

the probability that a randomly selected item has neither D1 nor D2 is 87%.

Explanation:

Let's use the formula for the probability of the complement event to calculate the probability that a randomly selected item has neither D1 nor D2:

P(neither D1 nor D2) = 1 - P(D1 or D2)

We know that 5% have D1, 10% have D2, and 2% have both defects. The probability of an item having D1 or D2 (or both) is:

P(D1 or D2) = P(D1) + P(D2) - P(D1 and D2)

where P(D1 and D2) represents the probability that an item has both D1 and D2, which is 2% in this case.

Substituting the given values, we get:

P(D1 or D2) = 5% + 10% - 2% = 13%

So the probability of an item having neither D1 nor D2 is:

P(neither D1 nor D2) = 1 - P(D1 or D2) = 1 - 13% = 87%

Therefore, the probability that a randomly selected item has neither D1 nor D2 is 87%.