a. The events are mutually exclusive, so
![P(A\cup B\cup C)=P(A)+P(B)+P(C)=\boxed{0.9}](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%5Ccup%20C%29%3DP%28A%29%2BP%28B%29%2BP%28C%29%3D%5Cboxed%7B0.9%7D)
b. For the same reason,
![P(A\cap B\cap C)=\boxed0](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%5Ccap%20C%29%3D%5Cboxed0)
Another way to see this is to use the result from part (a), and the inclusion/exclusion principle:
![P(A\cap B\cap C)=P(A)+P(B)+P(C)-P(A\cup B\cup C)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%5Ccap%20C%29%3DP%28A%29%2BP%28B%29%2BP%28C%29-P%28A%5Ccup%20B%5Ccup%20C%29)
and the right side reduces to 0.
c. Same as (b),
![P(A\cap B)=\boxed0](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D%5Cboxed0)
d. Same as (b),
![P((A\cup B)\cap C)=\boxed0](https://tex.z-dn.net/?f=P%28%28A%5Ccup%20B%29%5Ccap%20C%29%3D%5Cboxed0)
We can also use the distributivity rule for unions and intersections to write
![P((A\cup B)\cap C)=P((A\cap C)\cup(B\cap C))=P(A\cap C)+P(B\cap C)=0](https://tex.z-dn.net/?f=P%28%28A%5Ccup%20B%29%5Ccap%20C%29%3DP%28%28A%5Ccap%20C%29%5Ccup%28B%5Ccap%20C%29%29%3DP%28A%5Ccap%20C%29%2BP%28B%5Ccap%20C%29%3D0)
e. If the
is the complement of
, then by DeMorgan's law,
![P(A'\cap B'\cap C')=P(A\cup B\cup C)'=1-P(A\cup B\cup C)=\boxed{0.1}](https://tex.z-dn.net/?f=P%28A%27%5Ccap%20B%27%5Ccap%20C%27%29%3DP%28A%5Ccup%20B%5Ccup%20C%29%27%3D1-P%28A%5Ccup%20B%5Ccup%20C%29%3D%5Cboxed%7B0.1%7D)
Answer:
30 students would have to go for the cost to be the same.
Step-by-step explanation:
Bus A: $40 + ($4 * 30) = $160
Bus B: $100 + ($2 * 30) = $160
In order to calculate that distance, we need to know the
" scale " of the map ... how many miles is represented by
1 inch on the map, or the ratio.
Different maps are drawn with different scales.
I did this on a calcalator 3÷5=0.6