PROBLEM SOLVING ON CONDITIONAL PROBABILITY AND PRODUCT RULE

Answer the following and show your complete solution

1. Rahul's two favorite foods are bagels and pizza. Let A represent the event that he eats a bagel for breakfast and B represents the event that he eats pizza for lunch. On a randomly selected day, the probability that Rahul will eat a bagel for breakfast, P(A), is 0.6, the probability that he will eat pizza for lunch, P(B), is equal to 0.5 and the conditional probability that he eats a bagel for breakfast, given that he eats pizza for lunch, P(A|B), is equal to 0.7.

What is the probability of P(BA)?

2. A company screens job applicants for illegal drug use at a certain stage in their hiring process. The specific test they use has a false positive rate of 2% and a false negative rate of 1%. Suppose that 5% all their applicants are actually using illegal drugs, and we randomly select an applicant.

Given the applicant tests positive, what is the probability that they are actually on drugs?

3. Researchers surveyed 100 students on which superpower they would most like to have. This two-way table displays data for the sample of students who responded to the survey:

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