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P(V|A) is not 0.95. It is opposite:
P(A|V)=0.95
From the text we can also conclude, that
P(A|∼V)=0.1
P(B|V)=0.9
P(B|∼V)=0.05
P(V)=0.01
P(∼V)=0.99
What you need to calculate and compare is P(V|A) and P(V|B)
P(V∩A)=P(A)⋅P(V|A)⇒P(V|A)=P(V∩A)P(A)
P(V∩A) means, that Joe has a virus and it is detected, so
P(V∩A)=P(V)⋅P(A|V)=0.01⋅0.95=0.0095
P(A) is sum of two options: "Joe has virus and it is detected" and "Joe has no virus, but it was mistakenly detected", therefore:
P(A)=P(V)⋅P(A|V)+P(∼V)⋅P(A|∼V)=0.01⋅0.95+0.99⋅0.1=0.1085
I did this equation and it’s A
-16t^2+400=0
16t^2=400
take square root on both sides.
4t=20
t=20/4
t=5
Square numbers are numbers with an odd number of factors. For example, 1 and 4 are square numbers.
