5 selected from batch of 50 produced, if one is found defective, than each is tested individually. Find the probability that the entire batch will need testing if the batch contains:
8 defective phones
2 defective phones
To find the probability that the entire batch will need testing, we need to consider the number of defective phones in the batch.
Case 1: The batch contains 8 defective phones.
In this case, if one defective phone is found among the 5 selected, then the entire batch of 50 phones will need testing. The probability of selecting a defective phone in the first test is 8/50. Once a defective phone is found, all 50 phones need to be individually tested, so the probability is 1.
Therefore, the probability that the entire batch will need testing if the batch contains 8 defective phones is (8/50) * 1 = 8/50.
Case 2: The batch contains 2 defective phones.
In this case, if one defective phone is found among the 5 selected, then the entire batch of 50 phones will not need testing. The probability of selecting a defective phone in the first test is 2/50. Once a defective phone is found, the remaining 4 phones can be assumed to be non-defective, so no further testing is required.
Therefore, the probability that the entire batch will need testing if the batch contains 2 defective phones is (2/50) * 1 = 2/50.
To summarize:
- If the batch contains 8 defective phones, the probability that the entire batch will need testing is 8/50.
- If the batch contains 2 defective phones, the probability that the entire batch will need testing is 2/50.