Suppose a software for statistical inference methods often sets the default probability of a correct inference to be 0.95.

Suppose we make an inference about the population proportion of people who like to go trekking, and we consider this separately for men and for women. LetAdenote the outcome that the inference about men is correct, and let B denote the outcome that the inference about women is correct. Treating these as independent samples and inferences, find the probability that both inferences are correct.