Two percent of the circuit boards manufactured by a particular company are defective. If circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is

To calculate the probability, we need to use the concept of geometric distribution. The geometric distribution models the number of trials required to achieve a success (finding a defective board) given a fixed probability of success (defect rate of 2%).

The probability of finding a defective board on any given trial is 2% or 0.02. Therefore, the probability of not finding a defective board on any given trial is 1 - 0.02 = 0.98.

Now, we want to find the probability of finding a defective board on the 10th trial. This means we need to have 9 consecutive non-defective boards followed by a defective board.

The probability of having 9 consecutive non-defective boards is calculated as (0.98)^9 = 0.8174 (rounded to 4 decimal places).

Finally, we multiply this probability by the probability of finding a defective board on the 10th trial, which is 0.02 (0.8174 * 0.02 = 0.0163, rounded to 4 decimal places).

Therefore, the probability that it takes 10 circuit boards to be inspected before a defective board is found is approximately 0.0163, or 1.63%.