Answer:
Case(a): ![p[b]=\frac{1}{3}p[a]](https://tex.z-dn.net/?f=p%5Bb%5D%3D%5Cfrac%7B1%7D%7B3%7Dp%5Ba%5D)
Case(b): ![p[b]=0](https://tex.z-dn.net/?f=p%5Bb%5D%3D0)
Case(c): ![p[b]=\frac{1}{2}p[a\cap b]](https://tex.z-dn.net/?f=p%5Bb%5D%3D%5Cfrac%7B1%7D%7B2%7Dp%5Ba%5Ccap%20b%5D)
Step-by-step explanation:
Given
(a) events a and b are a partition and p[a] = 3p[b].
(b) for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.
(c) for events a and b, p[a ∪ b] = p[a]− p[b].
we have to find the p[b] in each case:
Case (a): events a and b are a partition and p[a] = 3p[b].
gives
Case (b): for events a and b, p[a ∪ b] = p[a] and p[a ∩ b] = 0.
![p[a\cup b]=p[a]](https://tex.z-dn.net/?f=p%5Ba%5Ccup%20b%5D%3Dp%5Ba%5D)
⇒![p[a]+p[b]-p[a\cap b]=p(a)](https://tex.z-dn.net/?f=p%5Ba%5D%2Bp%5Bb%5D-p%5Ba%5Ccap%20b%5D%3Dp%28a%29)
⇒ ∵ p[a ∩ b] = 0.
Case(3): for events a and b, p[a ∪ b] = p[a]− p[b].
p[a ∪ b] = p[a]− p[b]
⇒ ![p[a]+p[b]-p[a\cap b]=p[a]-p[b]](https://tex.z-dn.net/?f=p%5Ba%5D%2Bp%5Bb%5D-p%5Ba%5Ccap%20b%5D%3Dp%5Ba%5D-p%5Bb%5D)
⇒ ![2p[b]=p[a\cap b]](https://tex.z-dn.net/?f=2p%5Bb%5D%3Dp%5Ba%5Ccap%20b%5D)
⇒
Answer:
(- 1, 3)
Step-by-step explanation:
To find the y- coordinate, substitute x = - 1 into the equation
y - 3 = 2(x + 1) ( add 3 to both sides )
y = 2(x + 1) + 3 ← substitute x = - 1
y = 2(- 1 + 1) + 3 = (2 × 0) + 3 = 0 + 3 = 3
15 I’m pretty sure but I don’t know
The equation would be y = 4x + 2 so just look with a graph that has a y-intercept of two, as well as moves up four and up 1 each time.
x / y
0 / 2
1 / 6
2/ 10
3 / 14
4 / 18
5 / 22
6 / 26
7 / 30
Answer:
It is <u><em>not </em></u>stay the same or get larger
Step-by-step explanation:
I'm sorry all i can do is eliminate options. I took the test twice and got it wrong both times. my next guess is that its impossible to tell but its a 50/'50 chance. I hope eliminating at least helps :(
