Question

The probability of a successful optical alignment in the assembly of an optical data storage product is 0.6. Assume the trials are independent. What is the probability that the first successful alignment requires exactly 2 trials?

Answer 1

The probability of a successful optical allignment in the assembly of an optical data storage product is 0.6.

So, the probability of an unsuccessful optical allignment, is (1-0.6), ie. 0.4.

Given that the trials are independent.

To find the probability that the first successful allignment requires exactly 2 trials.

Now, we are going to have the first successful allignment, in exactly two trials; this means that the first trial must be a failure, with probability 0.4; and the second trial would be a success, with probability 0.6.

Now, these two trials are independent.

So, the required probability is product of the two probabilities, ie.

So, the proabability that the first successful trial requires exactly 2 trials, is 0.24.