8 In a laboratory, two experiments are repeated every day of the week in different rooms until at least one is successful, the probability of success being p for each experiment. Supposing that the experiments in different rooms and on different days are performed independently of each other, what is the probability that the laboratory scores its first successful experiment on day n

The chance of having a success on day n is 1 minus the chance of not having a success ( assuming it doesn't matter if both have a success or just one has a success). The chance of not having a success on day n is q^2.

Step-by-step explanation:

In order to understand the above answer let us consider the following example:

In a laboratory, two experiments are repeated every day of the week in  different rooms until at least one is successful, the probability of success being  30% for each experiment. Supposing that the experiments in different rooms and on different days are performed independently of each other, what is the  probability that the laboratory scores its first successful experiment on day 10?

The first 9 days (18 experiments) have to be unsuccessful to have the first successful one on day 10. Therefore the probability of the first 18 experiments being unsuccessful is 0.7^18 = 0.1628% and the probability of being successful on day 10 is 1-(0.7^2) = 51%. Multiply those two together to get 0.083%.