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
Blababa [14]
3 years ago
8

Lucy offers to play the following game with Charlie: "Let us show dimes to each other, each choosing either heads or tails. If w

e both show heads, I pay you $3. If we both show tails, I pay you $1. If the two don’t match, you pay me $2." Charlie reasons as follows. "The probability of both heads is 1/4, in which case I get $3. The probability of both tails is 1/4, in which case I get $1. The probability of no match is 1/2, and in that case I pay $2. So it is a fair game." Is he right? If not, (a) why not, and (b) what is Lucy’s expected profit from the game?
Mathematics
1 answer:
Darya [45]3 years ago
7 0

Answer:

(a)Charlie is right

(b)$0

Step-by-step explanation:

(a)A game is said to be a fair game when the probability of winning is equal to the probability of losing. Mathematically, a game is said to be fair when the expected value is zero.

In the game, the possible outcomes are: HH, HT, TH and TT.

Charlie wins when the outcome is HH, TT

  • P(Charlie Wins)=2/4
  • P(Charlie Losses)=2/4

Lucy wins when the outcome is HT or TH

  • P(Lucy Wins)=2/4
  • P(Lucy Losses)=2/4

Therefore, the game is fair. Charlie is right.

(b)

If the outcome is HH, Lucy pays $3.

If the outcome is HT or TH, Lucy gets $2.

If the outcome is TT, Lucy pays $1.

The probability distribution of Lucy's profit is given below:

\left|\begin{array}{c|c|c|c}$Profit(x)&-\$3&-\$1&\$2\\P(x)&1/4&1/4&2/4\end{array}\right|

Expected Profit

=(-3 \times \frac14)+(-1\times \frac14)+(2 \times \frac24)\\=$0

Lucy's expected profit from the game is $0.

You might be interested in
ANSWER THIS URGENTLY
neonofarm [45]
I think B if not type 1/3 pi 6 squared and add 6.71 or something with the 6.71
8 0
3 years ago
How do you factor this polynomial as a product of more than two factors?<br> x3+8x2+15x
umka21 [38]
x^3+8x^2+15x =\\&#10;x(x^2+8x+15)=\\&#10;x(x^2+3x+5x+15)=\\&#10;x(x(x+3)+5(x+3))=\\&#10;x(x+5)(x+3)&#10;
7 0
3 years ago
I need help it’s hard
Reika [66]

9514 1404 393

Answer:

  f^-1(x) = (x +4)/3

Step-by-step explanation:

The inverse function is found by swapping x and y, then solving for y.

  y = 3x -4 . . . . . function y = f(x)

  x = 3y -4 . . . . . inverse relation

  x +4 = 3y . . . . add 4

  (x +4)/3 = y . . . divide by 3. This is the inverse function

  f^-1(x) = (x +4)/3

6 0
3 years ago
An important factor in selling a residential property is the number of times real estate, agents show a home. A sample of 21 hom
Natalka [10]

Using the t-distribution to build the 99% confidence interval, it is found that:

  • The margin of error is of 3.64.
  • The 99% confidence interval for the population mean is (19.36, 26.64).

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

\overline{x} \pm t\frac{s}{\sqrt{n}}

In which:

  • \overline{x} is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 21 - 1 = 20 df, is t = 2.086.

The other parameters are given as follows:

\overline{x} = 23, s = 8, n = 21

The margin of error is given by:

M = t\frac{s}{\sqrt{n}} = 2.086\frac{8}{\sqrt{21}} = 3.64

Hence the bounds of the interval are:

\overline{x} - M = 23 - 3.64 = 19.36

\overline{x} + M = 23 + 3.64 = 26.64

The 99% confidence interval for the population mean is (19.36, 26.64).

More can be learned about the t-distribution at brainly.com/question/16162795

#SPJ1

7 0
2 years ago
Please help I'm stuck :/
Serggg [28]
Easy so just Take 4.50 and I said by 1.50 which one you're going to get three more bags of three need times it by 108÷10 and then that will just be one box and then all you have to do is just find the other boxes with that number so
3 0
2 years ago
Read 2 more answers
Other questions:
  • Using the given zero, find all other zeros of f(x).
    5·1 answer
  • Help I don't understand
    12·1 answer
  • 15 points
    5·2 answers
  • A book club has 10 members.How many ways can they choose a president, vice president, and secretary from among the members?
    11·2 answers
  • Will qamar have enough lacquer to cover the floor below? Please help I have been stuck on this for three days!!!
    14·1 answer
  • Name an object around your house that consists of three or more shapes. The only answer you can't use is a bike and the object c
    15·1 answer
  • Find the radius of the circle of the shaded sector has an area of 5pi and a central angle of 2pi/5 rads Please include steps !!!
    14·2 answers
  • On circle O below, the measure of SV is 120°.
    15·1 answer
  • Find y intercept of the linear equation y-5=2(x-4)
    15·1 answer
  • Please help me solve this...
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!