Mathematics, 30.01.2020 20:54 harding7807

Derek and mia place two green marbles and one yellow marble in a bag. somebody picks a marble out of the bag without looking and records its color (g for green and y for yellow). they replace the marble and then pick another marble. if the two marbles picked have the same color, derek loses 1 point and mia gains 1 point. if they are different colors, mia loses 1 point and derek gains 1 point. what is the expected value of the points for derek and mia?

Answers: 2

Show answers

Answers

Answer from: jules8022

Thus, the expected value of points for Derek and Mia are $\dfrac{-1}{9}$ and $\dfrac{1}{9}$ respectively.

Step-by-step explanation:

Number of green marbles = 2 and Number of Yellow marbles = 1

Then, total number of marbles = 2+1 = 3

A person selects two marbles one after another after replacing them.

So, the probabilities of selecting different combinations of colors are,

$1.\ P(GG)=P(G)\times P(G)\\\\P(GG)=\dfrac{2}{3}\times \dfrac{2}{3}\\\\P(GG)=\dfrac{4}{9}$

$2.\ P(GY)=P(G)\times P(Y)\\\\P(GY)=\dfrac{2}{3}\times \dfrac{1}{3}\\\\P(GY)=\dfrac{2}{9}$

$3.\ P(YG)=P(Y)\times P(G)\\\\P(YG)=\dfrac{1}{3}\times \dfrac{2}{3}\\\\P(YG)=\dfrac{2}{9}$

$4.\ P(YY)=P(Y)\times P(Y)\\\\P(YY)=\dfrac{1}{3}\times \dfrac{1}{3}\\\\P(YY)=\dfrac{1}{9}$

Now, we have that,

If two marbles are of same color, then Mia gains 1 point and Derek loses 1 point.

If two marbles are of different color, then Derek gains 1 point and Mia loses 1 point.

Also, the expected value of a random variable X is $E(X)=\sum_{i=1}^{n} x_i\times P(x_i)$ .

Then, the expected value of points for Derek is,

$E(D)= (-1)\times \dfrac{4}{9}+1\times \dfrac{2}{9}+1\times \dfrac{2}{9}+(-1)\times \dfrac{1}{9}\\\\E(D)= \dfrac{-5}{9}+\dfrac{4}{9}\\\\E(D)=\dfrac{-1}{9}$

And the expected value of points for Mia is,

$E(M)= 1\times \dfrac{4}{9}+(-1)\times \dfrac{2}{9}+(-1)\times \dfrac{2}{9}+1\times \dfrac{1}{9}\\\\E(M)= \dfrac{5}{9}-\dfrac{4}{9}\\\\E(M)=\dfrac{1}{9}$ .

Thus, the expected value of points for Derek and Mia are $\dfrac{-1}{9}$ and $\dfrac{1}{9}$ respectively.

Answer from: paulinahunl17

P(GG)= 4/9

P(GY)= 2/9

P(YG)= 2/9

P(YY)= 1/9

Derek, E(X) = -1/9

Mia, E(X) = 1/9

Step-by-step explanation: just did it on edge

Answer from: Quest

108

Answer from: Quest

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! : )

cretdit to source

Another question on Mathematics

Mathematics, 21.06.2019 16:00

The classrooms are trying to raise $1,200.00 for charity. mrs. leblanc's class has raised 50%. mr. patel's class has raised $235.14 ms. warner's class has raised 1/3 as much as mrs. leblanc's class. how much more money is needed to reach the goal of $1,200.00?

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Scott’s bank account showed a balance of $750 on sunday. during the next five days, he made one deposit of $140 and numerous withdrawals of $180 each. let x represent the number of withdrawals that scott made. write an inequality that can be used to find the maximum number of withdrawals that scott could have made and maintain a balance of at least $100. do not use a dollar sign ($) in your response.

Answers: 1

Answer

Mathematics, 22.06.2019 03:30

Lisette takes an ela exam and got 16 out of 27 questions correct. what percentage of the questions did lisette get correct?

Answers: 1

Answer

Mathematics, 22.06.2019 06:20

Which formula can be used to describe the sequence? -81 ,108,-144,192

Answers: 2

Answer

You know the right answer?

Derek and mia place two green marbles and one yellow marble in a bag. somebody picks a marble out of...