There are three power plants [x, y, z] that at any given time each one either generates electricity or idles. event a is that plant x is always idles. event b is that at least two plants generate electricity. p(a∩b) is 15% and probability of complement of aub is 6%. all outcomes in event a are equally likely. compute the probability of the event b?

We're told that

where the last fact is due to the law of total probability:

so that and are complementary.

By definition of conditional probability, we have

We make use of the addition rule and complementary probabilities to rewrite this as

By the law of total probability,

and substituting this into gives

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204