Final answer:
The probability that more than 10 non-defective motherboards are inspected before finding a defective one, with a 5% defect rate, is approximately 0.599, using the survival function of the geometric distribution.
Step-by-step explanation:
The student has asked a probability question related to finding the likelihood that more than 10 non-defective motherboards are inspected before a defective one is found, given that 5% of motherboards are defective. This is a geometric distribution scenario where if we let X be the number of motherboards checked until a defective one is discovered, finding the probability that X > 10 can be calculated using the survival function (1 - p)x, where p is the probability of finding a defective motherboard, which in this case is 0.05.
To calculate the probability that more than 10 inspections occur before finding a defective motherboard, we apply the formula: (1 - 0.05)10 = 0.9510. This calculation gives us the probability that the first 10 motherboards are not defective. After computing the value, we find that it is approximately 0.599, which means option a. 0.599 is the correct answer to the student's question.