A company has 500 employees, and 60% of them have children. Suppose that we randomly select 4 of these employees. What is the probability that exactly 3 of the 4 employees selected have children? We know that 300 of these employees have children. I tried to figure it out, how to work with the binomial equation by the given's

cuuhorre76 2022-09-12 Answered
A company has 500 employees, and 60% of them have children.
Suppose that we randomly select 4 of these employees.
What is the probability that exactly 3 of the 4 employees selected have children?
We know that 300 of these employees have children.
I tried to figure it out, how to work with the binomial equation by the given's
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Answers (1)

Julianna Crawford
Answered 2022-09-13 Author has 8 answers
Step 1
The probability that the first person picked has kids is 300 500 . Conditional on that, the probability that the second person picked has kids is 299 499 . Conditional on all that, the probability the third person has kids is 298 498 . Conditional on all that, the probability the fourth person doesn't have kids is 200 497 . So multiply these together and scale by 4 (since the person without kids could have been any of the four).
Step 2
An alternative perspective: the number of quadruples where exactly three have kids is ( 300 3 ) ( 200 1 ) . There are ( 500 4 ) quadruples in total, so divide the two to get the probability.

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Question on designing a state observer for discrete time system
I came through this problem while studying for an exam in control systems:
Consider the following discrete time system
x ( k + 1 ) = A x ( k ) + b u ( k ) , y ( k ) = c x ( k )
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Find a feedback regulation (if there is any) of the form u ( k ) = K x ^ ( k ) where x ^ ( k ) is the country estimation vector that is produced via a linear complete-order state observer such that the nation of the system and the estimation blunders e ( k ) = x ( k ) x ^ ( k ) go to zero after a few finite time. layout the kingdom observer and the block diagram.
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it is clean that the eigenvalues of the machine are λ 1 = 2 , λ 2 = g (consequently it is not BIBO solid) and that the pair (A,b) is controllable for every fee of g, as nicely a the pair (A,c) is observable for all values of g. consequently we will shift the eigenvalues with the aid of deciding on a benefit matrix okay such that our device is strong, i.e. it has its eigenvalues inside the unit circle | z | = 1.
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[ x ( k + 1 ) e ( k + 1 ) ] T = [ A b K B k O A L C ] [ x ( k ) e ( k ) ] T
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I want to ask the following:
Is my approach correct? Should I select the eigenvalues myself since I am asked to design the observer or should I just solve the characteristic equation and impose | λ 1 , 2 | < 1?
Should I determine L matrix as well since the error must also vanish? (because it is not asked)