To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original
function .
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Apply that on your function
Answer:
0.967 = 96.7% probability the rock sample actually contains raritanium
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive reading
Event B: Contains raritanium
Probability of a positive reading:
98% of 13%(positive when there is raritanium).
0.5% of 100-13 = 87%(false positive, positive when there is no raritanium). So
Positive when there is raritanium:
98% of 13%
What is the probability the rock sample actually contains raritanium?
0.967 = 96.7% probability the rock sample actually contains raritanium