Mathematics: What is the probability that the system does not have a type 2defect?b.What is the probability that the system has both type 1 and type 2 defects?c.Given that the system has a type 2defect, what is the probability that is has a type 1defect?

What is the probability that the system does not have

Oso29

19.01.2022

a. 0.93 b. 0.06 c. 0.05

Step-by-step explanation:

Probability is commonly known as the chance of success of a particular event. The probability of failure of the event can also be estimated.

(a) Probability of not having type 2 defect is: $P(A_{2}^{'})$ $= 1 - P(A_{2})$ = 1 - 0.07 = 0.93

(b) Probability of having type 1 and 2 defects is: $P(A_{1} n A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1}U A_{2}) = 0.12 + 0.07 - 0.13 = 0.06$

$P(A_{1} + A_{2} + A^{'} _{3}) = P(A_{1} n A_{2}) - P(A_{1} n A_{2} n A_{3}) = 0.06 - 0.01 = 0.05$

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mmimay3501

05.05.2020

x = 8

Step-by-step explanation:

When cutting the wire we will get two pieces

x and 12 - x

If we build a circle whith x , the lenght of the circle will be x, and if we look at the equation for a lenght of a cicle 2*π*r = x

then r = x/2π

and consequentely A₁ = area of a circle = πr² A₁ = π*x/2π

A₁ = x/2

With the other piece 12 - x we have to make an square so wehave to divide that piece in four equal length

side of the square = s

s = 1/4 ( 12 - x ) and the area is A₂ = [1/4 ( 12 - x)]²

A₂ = ( 12 - x )²/16

Then A₁ + A₂ = A(t) and this area as fuction of x

A (x) = x/2 + 1/16 ( 144 + x² -24x) A (x) =[ (8x + 144 + x² -24x)]/16

Taken derivatives in both sides

A´(x) = 8 + 2x - 24 = 0

2x -16 = 0 x = 8 and s = 12 - 8 s = 4

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