Problem (11), 10 points 3 Math majors and 3 Computer Science majors will be presenting at a conference. Three students will be randomly selected to present on Monday, and the remaining three stu- dents will present on Tuesday. (a, 3 points) What is the probability that two Computer Science majors and a math major will present on Tuesday? You do not need to simplify your answer.
(b, 5 points) Suppose we know at least one Math major has been selected to present on Monday. What is the probability that two Computer Science majors and a math major will present on Tuesday, given this information?
(c, 2 points) Based on your answer for b, are the events ‘at least one math major is selected to present on Monday' and 'two computer science majors and a math major present on Tuesday' independent?

a}

b)

c) NOT INDEPENDENT

Step-by-step explanation:

From the question we are told that

Sample space

Math majors are 3

computer science majors are 3

Generally the sample space is

Mathematically the sample space required on Monday is given as  

where =sample space on Monday

Therefore,

=

b)

Generally the the equation is given as

where

x  is  selecting two math major and 1 computer science major on Monday

y is at leas one math major selected

c)

Generally in representing independent events

=>

Mathematically

therefore

This does not satisfy the two equations stated above therefore NOT INDEPENDENT

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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