P(A and B)=P(A)* P(B)From the exercise we know the probability of a student being male and the probability that a student walks to school. However, we need to know the probability that a student does not walk to school. This can be determined by calculating the complement of P(walks).
To get to school, you have to either walk or get there by any other means.
P(walks)+P(any other means)=1
Therefore, the probability of selecting a student that either walks to school or does not walk to school is 100 %, because everybody has to get to school somehow.
d
Let's discuss the different sample spaces one at a time.
Part B
We calculated the probability that a student is a male and does not walk to school. The selected students should fulfill both of these criteria. Therefore, the sample space in Part B is the intersection of these events.
Part C
In Part C, we calculated the probability that a student walks to school or does not walk to school. The selected student has to fill either of these criteria. Therefore, the sample space in Part C is the union of these events.
