Answer:
B
Step-by-step explanation:
11/4=2.75
3/4=0.75
5/4=1.25
23/4=5.75
Answer:
540 degrees
Step-by-step explanation:
The numbers of choices in each category are multiplied together. We assume the order of paint choices matters: using color 1 in area A and color 2 in area B is not the same as using color 2 in area A and color 1 in area B.
P(7,2)*4*3*2 = 42*4*3*2 = 1008 ways
_____
P(n, k) = n!/(n-k)!
P(7, 2) = 7*6 = 42
Answer:
a) ![P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4](https://tex.z-dn.net/?f=%20P%28A%29%20%3DP%28a%29%2BP%28b%29%20%2BP%28c%29%3D%200.1%2B0.1%2B0.2%20%3D%200.4)
b) ![P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8](https://tex.z-dn.net/?f=%20P%28B%29%20%3DP%28c%29%20%2BP%28d%29%2BP%28e%29%3D0.2%2B0.4%2B0.2%3D0.8)
c) ![P(A') = 1-P(A) =1-0.4=0.6](https://tex.z-dn.net/?f=%20P%28A%27%29%20%3D%201-P%28A%29%20%3D1-0.4%3D0.6)
d) ![P(A \cup B) =0.4 +0.8-0.2 =1.0](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D0.4%20%2B0.8-0.2%20%3D1.0)
e) The intersection between the set A and B is the element c so then we have this:
![P(A \cap B) = P(c) =0.2](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28c%29%20%3D0.2)
Step-by-step explanation:
We have the following space provided:
![S= [a,b,c,d,e]](https://tex.z-dn.net/?f=%20S%3D%20%5Ba%2Cb%2Cc%2Cd%2Ce%5D)
With the following probabilities:
![P(a) =0.1, P(b)=0.1, P(c) =0.2, P(d)=0.4, P(e)=0.2](https://tex.z-dn.net/?f=P%28a%29%20%3D0.1%2C%20P%28b%29%3D0.1%2C%20P%28c%29%20%3D0.2%2C%20P%28d%29%3D0.4%2C%20P%28e%29%3D0.2)
And we define the following events:
A= [a,b,c], B=[c,d,e]
For this case we can find the individual probabilities for A and B like this:
![P(A) = 0.1+0.1+0.2 = 0.4](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.1%2B0.1%2B0.2%20%3D%200.4)
![P(B) =0.2+0.4+0.2=0.8](https://tex.z-dn.net/?f=%20P%28B%29%20%3D0.2%2B0.4%2B0.2%3D0.8)
Determine:
a. P(A)
![P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4](https://tex.z-dn.net/?f=%20P%28A%29%20%3DP%28a%29%2BP%28b%29%20%2BP%28c%29%3D%200.1%2B0.1%2B0.2%20%3D%200.4)
b. P(B)
![P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8](https://tex.z-dn.net/?f=%20P%28B%29%20%3DP%28c%29%20%2BP%28d%29%2BP%28e%29%3D0.2%2B0.4%2B0.2%3D0.8)
c. P(A’)
From definition of complement we have this:
![P(A') = 1-P(A) =1-0.4=0.6](https://tex.z-dn.net/?f=%20P%28A%27%29%20%3D%201-P%28A%29%20%3D1-0.4%3D0.6)
d. P(AUB)
Using the total law of probability we got:
![P(A \cup B) =P(A) +P(B)-P(A \cap B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3DP%28A%29%20%2BP%28B%29-P%28A%20%5Ccap%20B%29)
For this case
, so if we replace we got:
![P(A \cup B) =0.4 +0.8-0.2 =1.0](https://tex.z-dn.net/?f=%20P%28A%20%5Ccup%20B%29%20%3D0.4%20%2B0.8-0.2%20%3D1.0)
e. P(AnB)
The intersection between the set A and B is the element c so then we have this:
![P(A \cap B) = P(c) =0.2](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28c%29%20%3D0.2)