Answer:
-4
Step-by-step explanation:
If anything the first thing you would want to do is covert your fraction so a decimal. (-4 1/2) as a decimal is -4.50. From there it would be easier to divide. to get an answer of -4
Answer:
$55.24
Step-by-step explanation:
Add $32.78 + $27.24 + $5.22
= 65.24
Subtract 10
= $55.24
(a) If
are mutually exclusive, then
![P(A\cap B)=P(A\cap C)=P(B\cap C)=P(A\cap B\cap C)=0](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28A%5Ccap%20C%29%3DP%28B%5Ccap%20C%29%3DP%28A%5Ccap%20B%5Ccap%20C%29%3D0)
so we have
![P(A\cup B\cup C)=P(A)+P(B)+P(C)=\dfrac{47}{60}](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%5Ccup%20C%29%3DP%28A%29%2BP%28B%29%2BP%28C%29%3D%5Cdfrac%7B47%7D%7B60%7D)
(b) If
are mutually independent, then
![P(A\cap B)=P(A)P(B),](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28A%29P%28B%29%2C)
![P(A\cap C)=P(A)P(C),](https://tex.z-dn.net/?f=P%28A%5Ccap%20C%29%3DP%28A%29P%28C%29%2C)
![P(B\cap C)=P(B)P(C),](https://tex.z-dn.net/?f=P%28B%5Ccap%20C%29%3DP%28B%29P%28C%29%2C)
![P(A\cap B\cap C)=P(A)P(B)P(C)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%5Ccap%20C%29%3DP%28A%29P%28B%29P%28C%29)
so that
![P(A\cup B\cup C)=P(A)+P(B)+P(C)-(P(A\cap B)+P(A\cap B)+P(B\cap C))+P(A\cap B\cap C)](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%5Ccup%20C%29%3DP%28A%29%2BP%28B%29%2BP%28C%29-%28P%28A%5Ccap%20B%29%2BP%28A%5Ccap%20B%29%2BP%28B%5Ccap%20C%29%29%2BP%28A%5Ccap%20B%5Ccap%20C%29)
![P(A\cup B\cup C)=\dfrac{47}{60}-\left(\dfrac1{12}+\dfrac1{15}+\dfrac1{20}\right)+\dfrac1{60}](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%5Ccup%20C%29%3D%5Cdfrac%7B47%7D%7B60%7D-%5Cleft%28%5Cdfrac1%7B12%7D%2B%5Cdfrac1%7B15%7D%2B%5Cdfrac1%7B20%7D%5Cright%29%2B%5Cdfrac1%7B60%7D)
![P(A\cup B\cup C)=\dfrac35](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%5Ccup%20C%29%3D%5Cdfrac35)