If Group A has 1/100 items defective, and Group B has 1/200 items defective.

What is the probability the second item inspected works given that the first one inspected also worked?

To find the probability that the second item inspected works given that the first one inspected also worked, we can use conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.

Let's break down the question and solve it step by step:

Step 1: Identify the given information:
- Group A has 1/100 items defective, which means the probability of an item from Group A being defective is 1/100. So, the probability of an item from Group A working is 1 - 1/100 = 99/100.
- Group B has 1/200 items defective, which means the probability of an item from Group B being defective is 1/200. So, the probability of an item from Group B working is 1 - 1/200 = 199/200.

Step 2: Define the events:
- Let A1 be the event that the first item inspected is from Group A and it works.
- Let A2 be the event that the second item inspected is from Group A and it works.
- Let B1 be the event that the first item inspected is from Group B and it works.
- Let B2 be the event that the second item inspected is from Group B and it works.

Step 3: Determine the probability of the second item from Group A working given that the first item from Group A worked:
- P(A1) is the probability of the first item from Group A working, which is 99/100.
- P(A2|A1) is the conditional probability of the second item from Group A working given that the first item from Group A worked.

Step 4: Simplify the conditional probability:
- P(A2|A1) represents the probability of A2 occurring given that A1 occurred. Since the items are independent of each other, the probability of the second item from Group A working is the same as the probability of a random item from Group A working, which is 99/100.

Therefore, the probability that the second item inspected works given that the first one inspected also worked is 99/100. So, the answer is 99/100.