1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rusak2 [61]
3 years ago
15

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

they are different colors, then you win -$1.00. (This is, you lose $1.00.) Calculate (a) the expected value of the amount you win; (b) the variance of the amount you win.
Mathematics
1 answer:
topjm [15]3 years ago
7 0

Answer:

a) The expected value is \frac{-1}{15}

b) The variance is  \frac{49}{45}

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is \binom{10}{2}.

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is \binom{5}{2}. Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is \binom{5}{1}\cdot \binom{5}{1}. So, we define the following probabilities.

Probability of winning: \frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}

Probability of losing \frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing =1.10\cdot  \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing =1.10^2\cdot  \frac{4}{9}+\frac{5}{9}=\frac{82}{75}

We will use the following formula

Var(X) = E(X^2)-E(X)^2

Thus

Var(X) = \frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}

You might be interested in
Hi bro sorry to bother you but I have a question it is ok . Ok then so 875x975=
mel-nik [20]

Answer:

853,125

Step-by-step explanation:

Umhhh u can use a calculator… or write it down and slowly break down solve it like that.

Hope this helps, good luck! ;)

4 0
3 years ago
Read 2 more answers
Is -9/4 rational. Please I need this now the thing said 20 characters long so I’m just gonna type. The best answer gets brainlie
mihalych1998 [28]

Answer:

no -9/4 is irrational

Step-by-step explanation:

vacsusvvsjshsvsh plz give brainliest

3 0
3 years ago
The graph at the right described the money two clubs are earning from fundraising. In how many weeks will the two clubs have the
pickupchik [31]

Answer:

52 weeks

Step-by-step explanation:

The club starting with $270 (club 1) is increasing their bank balance each week by ...

... $280 -270 = $10

The club starting with $10 (club 2) is increasing their bank balance each week by ...

... $25 -10 = $15

Club 2 is gaining on Club 1 by $15 -10 = $5 each week. So, the initial difference of $270 -10 = $260 will be overcome in ...

... $260/($5/week) = 52 weeks

_____

The same result is shown in the attached graph, which also shows that both clubs' bank balances will be $790 at that time.

7 0
3 years ago
Which function is equivalent to g ( x ) = x 2 + 15 x - 54?
svetoff [14.1K]

Answer:

I have solved on my own.

contains the answer to your question.

6 0
3 years ago
Read 2 more answers
Write 0.57 as a fraction in simplest form.<br> 0.57 <br> Lower number fraction
krek1111 [17]

Answer:

14.25/25

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Analyze the diagram below and complete the instructions that follow.
    9·2 answers
  • A hairdresser is deciding where to open her own studio. If the hairdresser chooses Location A, she will pay $1200 per month in r
    12·1 answer
  • 270 is 90% of what number?
    6·1 answer
  • Question 5 of 13, Step 1 of 1
    9·1 answer
  • Which expression has a value of 36?
    10·2 answers
  • Square Root Of 0.36 is<br> 1. 0.6<br> 2. 0.06<br> 4. 1.8<br> 5. 0.18<br><br> please Help me
    5·2 answers
  • A turtle is at the bottom of a 14 foot well. Each day it crawls up 5 feet, but each night it slips back 4 feet. After how many d
    6·1 answer
  • Solve this problem.
    12·1 answer
  • Help me with this question please! Do this ASAP!
    8·2 answers
  • A rectangular prism is made up of cubes. The prism is 8
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!