Answer:
a. 0.5855
b. 0.6354
c. 0.0676
Step-by-step explanation:
Be the events:
E: The product is highly successful
ME: The product is moderately successful
P: The product is poorly successful
B: The product received good reviews
MB: The product received bad reviews
You have then:
![P(E) = 0.4000](https://tex.z-dn.net/?f=P%28E%29%20%3D%200.4000)
![P(ME) = 0.3500](https://tex.z-dn.net/?f=P%28ME%29%20%3D%200.3500)
![P(P) = 0.2500](https://tex.z-dn.net/?f=P%28P%29%20%3D%200.2500)
and ![P(MB|E) = 1 - P(B|E) = 1 - 0.9300 = 0.0700](https://tex.z-dn.net/?f=P%28MB%7CE%29%20%3D%201%20-%20P%28B%7CE%29%20%3D%201%20-%200.9300%20%3D%200.0700)
![P(P|E) = 0.1400](https://tex.z-dn.net/?f=P%28P%7CE%29%20%3D%200.1400)
a. invoking the total probability theorem, you have:
![P(B) = P(B|E)P(E) + P(B|ME)P(ME) + P(B|P)P(P) = (0.9300)(0.4000) + (0.5100)(0.3500) + (0.1400)(0.2500) = 0.5855](https://tex.z-dn.net/?f=P%28B%29%20%3D%20P%28B%7CE%29P%28E%29%20%2B%20P%28B%7CME%29P%28ME%29%20%2B%20P%28B%7CP%29P%28P%29%20%3D%20%280.9300%29%280.4000%29%20%2B%20%280.5100%29%280.3500%29%20%2B%20%280.1400%29%280.2500%29%20%3D%200.5855)
b. invoking the Baye's theorem, you have:
![P(E|B) = \frac{P(B|E)P(E)}{P(B)} = \frac{(0.9300)(0.4000)}{0.5855} = 0.6354](https://tex.z-dn.net/?f=P%28E%7CB%29%20%3D%20%5Cfrac%7BP%28B%7CE%29P%28E%29%7D%7BP%28B%29%7D%20%3D%20%5Cfrac%7B%280.9300%29%280.4000%29%7D%7B0.5855%7D%20%3D%200.6354)
c. Using the result obtained in a.
, then:
![P(E|MB) = \frac{P(MB|E)P(E)}{P(MB)} = \frac{(0.0700)(0.4000)}{0.4145} = 0.0676](https://tex.z-dn.net/?f=P%28E%7CMB%29%20%3D%20%5Cfrac%7BP%28MB%7CE%29P%28E%29%7D%7BP%28MB%29%7D%20%3D%20%5Cfrac%7B%280.0700%29%280.4000%29%7D%7B0.4145%7D%20%3D%200.0676)
F(x) = 3x^2 + 4x - 1
f(-3) = 3(-3)^2 + 4(-3) - 1
f(-3) = 3 * 9 - 12 - 1
f(-3) = 27 - 12 - 1
f(-3) = 15 - 1
f(-3) = 14
Answer:
15
Step-by-step explanation:
Let n represent the number of twelvths in 5/4.
Expressed symbolically, this is n/12 = 5/4.
The LCD is 12. Multiply numerator and denominator of 5/4 by 3, obtaining:
n/12 = 15/12. Then n = 15.
There are 15 twelves in 5/4.
Store: $8.99
Brand one: $7.75
Brand two: $9.77