For a class activity, your group has been assigned the task of generating a quiz question that requires use of the formula for conditional probability to compute P(B | A). Your group comes up with the following question "If P(A and B) = 0.40 and P(A) = 0.20, what is the value of P(B | A)?" What is wrong with this question? Hint: Consider the answer you get when using the correct formula, P(B | A) = P(A and B)/P(A). P(A and B) cannot be greater than P(A), because this yields a probability greater than 1 for the answer. P(A and B) should be larger.     P(A and B) cannot be greater than P(A), because this yields a probability less than 0 for the answer. The question should be looking for P(A | B) not P(B | A).

Foreign freshmen are required to take an English placement exam. Over the past several years, 20% of the new students have failed the test and have been placed in remedial classes. In a sample of n = 100 studentsfrom this year’s class, only 12 failed the test.

Find P(A and B). (Give your answer correct to two decimal places.) A and B are independent events, P(A) = 0.46 and P(B) = 0.52

A restaurant owner wanted to know which time range are popular among the customers. Data were collected on the following events:  L = a customer usually visits the restaurant during lunch time D = a customer usually visits the restaurant during dinner time Data collected suggest the following:  P( L ) = 0.6 P( D ) = 0.7 P( L and D) = 0.3 What is the possibility that a customer only visit the restaurant during dinner time