A train station has installed a system for determining whether bags contain explosives. It has a 95% chance of correctly identifying a bag containing explosives (5% chance of a false negative), and a 99.5% chance of correctly classifying a bag without explosives as safe (0.5% chance of a false positive). Suppose that the train station screens 4 million bags per year, and that 10 of these bags are expected to contain explosives. (2.5x10-6 probability that a bag contains explosives)A bag is identified by the system as containing explosives. What’s the probability that it actually contains explosives?If we want the probability in part (a) to be at least 0.5, what should the probability of correctly identifying a bag without explosives be?Would it be possible to make the probability in part (a) at least 0.5 by increasing the chance of correctly identifying bags containing explosives? Justify your answerThe probability of identifying a bag with explosives correctly is 95%the probability of identifying a bag without explosives as safe is 99.5%Given a sample space of 4 million, there are 10 bags that are expected to contain explosivesThis is all the info the problem gives me

a) P(identified as containing explosives)=P(actually contains explosives and identified as containing explosives)+P(actually not contains explosives and identified as containing explosives)

=(10/(4*106))*0.95+(1-10/(4*106))*0.005 =0.005002363

hence  probability that it actually contains explosives given identified as containing explosives)

=(10/(4*106))*0.95/0.005002363=0.000475

b)

let probability of correctly identifying a bag without explosives be a

hence a =0.99999763 ~ 99.999763%

c)

No as even if that becomes 1 ; proportion of true explosives will always be less than half of total explosives detected,

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.