Answer and Step-by-step explanation:
The computation is shown below:
Let us assume that
Spam Email be S
And, test spam positive be T
Given that
P(S) = 0.3
![P(\frac{T}{S}) = 0.95](https://tex.z-dn.net/?f=P%28%5Cfrac%7BT%7D%7BS%7D%29%20%3D%200.95)
![P(\frac{T}{S^c}) = 0.05](https://tex.z-dn.net/?f=P%28%5Cfrac%7BT%7D%7BS%5Ec%7D%29%20%3D%200.05)
Now based on the above information, the probabilities are as follows
i. P(Spam Email) is
= P(S)
= 0.3
![P(S^c) = 1 - P(S)](https://tex.z-dn.net/?f=P%28S%5Ec%29%20%3D%20%201%20-%20P%28S%29)
= 1 - 0.3
= 0.7
ii. ![P(\frac{S}{T}) = \frac{P(S\cap\ T}{P(T)}](https://tex.z-dn.net/?f=P%28%5Cfrac%7BS%7D%7BT%7D%29%20%3D%20%5Cfrac%7BP%28S%5Ccap%5C%20T%7D%7BP%28T%29%7D)
![= \frac{P(\frac{T}{S}) . P(S) }{P(\frac{T}{S}) . P(S) + P(\frac{T}{S^c}) . P(S^c) }](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BP%28%5Cfrac%7BT%7D%7BS%7D%29%20.%20P%28S%29%20%7D%7BP%28%5Cfrac%7BT%7D%7BS%7D%29%20.%20P%28S%29%20%2B%20P%28%5Cfrac%7BT%7D%7BS%5Ec%7D%29%20.%20P%28S%5Ec%29%20%7D)
![= \frac{0.95 \times 0.3}{0.95 \times 0.3 + 0.05 \times 0.7}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B0.95%20%5Ctimes%200.3%7D%7B0.95%20%5Ctimes%200.3%20%2B%200.05%20%5Ctimes%200.7%7D)
= 0.8906
iii. ![P(\frac{S}{T^c}) = \frac{P(S\cap\ T^c}{P(T^c)}](https://tex.z-dn.net/?f=P%28%5Cfrac%7BS%7D%7BT%5Ec%7D%29%20%3D%20%5Cfrac%7BP%28S%5Ccap%5C%20T%5Ec%7D%7BP%28T%5Ec%29%7D)
![= \frac{P(\frac{T^c}{S}) . P(S) }{P(\frac{T^c}{S}) . P(S) + P(\frac{T^c}{S^c}) . P(S^c) }](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BP%28%5Cfrac%7BT%5Ec%7D%7BS%7D%29%20.%20P%28S%29%20%7D%7BP%28%5Cfrac%7BT%5Ec%7D%7BS%7D%29%20.%20P%28S%29%20%2B%20P%28%5Cfrac%7BT%5Ec%7D%7BS%5Ec%7D%29%20.%20P%28S%5Ec%29%20%7D)
![= \frac{(1 - 0.95)\times 0.3}{ (1 -0.95)0.95 \times 0.3 + (1 - 0.05) \times 0.7}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%281%20-%200.95%29%5Ctimes%200.3%7D%7B%20%281%20-0.95%290.95%20%5Ctimes%200.3%20%2B%20%281%20-%200.05%29%20%5Ctimes%200.7%7D)
= 0.0221
We simply applied the above formulas so that the each part could come
Answer (least to greatest):
- -2.4
- -2.25
- -11/5
- 15/10
- 1.6
I hope this helps!
Answer:
55 days
Step-by-step explanation:
Given
Jim ran 15 miles in 5 days
no. of miles ran in 5 days = 15 miles
dividing LHS and RHS by 5
no. of miles ran in 5/5(=1) days = 15/5 miles = 3 miles
no. of miles ran in 1 day = 3 miles
let the no. of days taken to run 165 miles be x ----A
No of miles ran in x days = x*no. of miles ran in 1 day = 3x miles
thus, From A
3x = 165
x = 165/3 = 55
Thus, it took 55 days for JIM to run 165 miles
Answer:
I can only answer when it is written with pencil
The slope of the inverse is 1/2.