d Consider the word and in Part B, and the word or in Part C.
A
a P=75 %
B
b P=15 %
C
c P=100 %
D
dPart B: Intersection
Part C: Union
Practice makes perfect
a From the exercise, we know that the probability of a student being male is 40 %. The probability of a student being female is the complement of this.
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).
c 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.
