Question

A group of students were asked if they carry a credit card and what color it is. The responses are listed in the table.

a) P(Student has a blue card and is a sophomore) = 8/86
b) P(Student has a red card | Student is a freshman) = 5/41
c) P(Student is a freshman | Student has a blue card) = 5/17
d) P(Student is a freshman or Student has a blue card) = (41+17-5)/86

Answer 1

The question relates to probability in mathematics, specifically conditional probability where we calculate the chance of one event given another event has already occurred.

Step-by-step explanation:

The question provided falls under the category of probability, specifically conditional probability and the use of probability rules. To find the probability of an event given another event (conditional probability), we use the formula P(A|B) = P(A AND B) / P(B), where P(A|B) is the probability of event A given that event B has occurred, P(A AND B) is the probability that both events occur, and P(B) is the probability of event B occurring. For the example provided about finding the probability that a student has change given they rode a bus, we would count all students who rode a bus for P(B) and from those, count how many students had change for P(A AND B), and use the formula to calculate P(A|B).