Answer:
False
Step-by-step explanation:
They are going to have a little 1.
Answer:
the probability the rock has raritanium is 0.9670
Step-by-step explanation:
These events have been defined as
Z: sample has raritanium
Y: the reading from detector is positive
Z': sample has no raritanium
Y': Reading from detector is negative
P(z) = 0.13
P(y'/z) = 0.02
P(y/z')= 0.005
We need to find p(z/y)
= p(z/y) = p(z ∩ y)/p(y)
= P(z) - p(z∩y)/0.13 = 0.02
Remember the value of p(z) = 0.13
So when we cross multiply we get
0.13 - p(z ∩ y) = 0.02 x 0.13
0.13 - p(z ∩ y) = 0.0026
-p(z ∩ y) = 0.0026 - 0.13
Such that
p(z ∩ y) = 0.1274
P(y/z')= 0.005
P(z∩y') = 0.005
Since p(z) = 0.13
P(z') = 1-0.13
P(y) - p(z∩y)/0.87 = 0.005
We cross multiply
P(y) - 0.1274 = 0.005x0.87
P(y) = 0.1274+0.00435
P(y) = 0.13175
We have 0.1274/0.13175
= 0.9670
So we conclude that probability rock has raritanium is 0.9670
