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
bezimeni [28]
2 years ago
6

The game of European roulette slots: 18 red, 18 black, and I green. A ball is spun onto the wheel and will eventually land ina s

lot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, thev pean roulette. The game of European roulette lose their money. (a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings? deviation of your total winnings? of the two games? (b) Suppose you bet $1 in three different rounds. What is the expected value and standard (c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness
Mathematics
1 answer:
Anestetic [448]2 years ago
5 0

Answer:

(a) E(x) = -0.081  S.D = 3

(b) E(x) = -0.081  S.D = 1.73

(c) it is less risky to bet $1 in three different rounds as compared to betting $3 in a single round.    

Step-by-step explanation:

(a) You bet $3 on a single round which means that if you win the game, your amount will double ($6), your profit will be $3. Whereas, if you lose the round, your profit will be -$3. You can only bet on red or black and both have 18 slots each.

So, the probability of landing the ball in a red/black slot = 18/37. This is the probability of winning. The probability of losing can be calculated as 1-18/37 = 19/37.

We can make a probability distribution table:

x                    3             -3

P(X=x)         18/37      19/37

Expected value E(x) can be calculated as:

E(x) = ∑ x.P(x)

      = (3)(18/37) + (-3)(19/37)

E(x) = -0.081

Standard deviation can be calculated by the following formula:

Var(x) = E(x²) - E(x)²

S.D = √Var(x)

We need to first calculate E(x²).

E(x²) = ∑x².P(x)

       = (3)²(18/37) + (-3)²(19/37)

       = (9)(18/37) + (9)(19/37)

E(x²) = 9

Var(x) = E(x²) - E(x)²

         = 9 - (-0.081)²

Var(x) = 8.993

S.D = √8.993

S.D = 2.99 ≅ 3

(b) Now, the betting price is $1 and 3 rounds are played. We will compute the expectation for one round and then add it thrice to find the expectation for three rounds. Similarly, for the standard deviations, we will add the individual variances and then consider the square root of it.

E(x) = ∑ x.P(x)

      = (1)(18/37) + (-1)(19/37)

E(x) = -0.027

Standard deviation can be calculated by the following formula:

Var(x) = E(x²) - E(x)²

S.D = √Var(x)

We need to first calculate E(x²).

E(x²) = ∑x².P(x)

       = (1)²(18/37) + (-1)²(19/37)

       = (1)(18/37) + (1)(19/37)

E(x²) = 1

Var(x) = E(x²) - E(x)²

         = 1 - (-0.027)²

Var(x) = 0.9992

The expectation for one round is -0.027

For three rounds,

E(x₁ + x₂ + x₃) = E(x₁) + E(x₂) + E(x₃)

                     = (-0.027) + (-0.027) + (-0.027)

E(x₁ + x₂ + x₃) = -0.081

Similarly, the variance for one round is 0.9992.

Var (x₁ + x₂ + x₃) = Var(x₁) + Var(x₂) + Var(x₃)

                           = 0.9992 + 0.9992 + 0.9992

Var (x₁ + x₂ + x₃) = 2.9976

S.D = √2.9976

S.D = 1.73              

(c) The expected values for both part (a) and (b) are the same but the standard deviation is lower in part (c) as compared to (b). Since the standard deviation is less in part (c), it means that it is <u>less risky to bet $1 in three different rounds as compared to betting $3 in a single round.</u>            

You might be interested in
What model for distributive properties Shows that 3(2x+4) is equivalent to 6x+12
Anestetic [448]
3(2x+6)
Will give you 6x+12
6 0
3 years ago
Read 2 more answers
What is the product of the polynomials below? (x-9)(x+2)
Leno4ka [110]
(x-9) (x+2)=x²+2x-9x-18=x²-7x-18
5 0
3 years ago
Read 2 more answers
At a college, 69% of the courses have final exams and 42% of courses require research papers. Suppose that 29% of courses have a
laila [671]

Answer:

a) 0.82

b) 0.18

Step-by-step explanation:

We are given that

P(F)=0.69

P(R)=0.42

P(F and R)=0.29.

a)

P(course has a final exam or a research paper)=P(F or R)=?

P(F or R)=P(F)+P(R)- P(F and R)

P(F or R)=0.69+0.42-0.29

P(F or R)=1.11-0.29

P(F or R)=0.82.

Thus, the the probability that a course has a final exam or a research paper is 0.82.

b)

P( NEITHER of two requirements)=P(F' and R')=?

According to De Morgan's law

P(A' and B')=[P(A or B)]'

P(A' and B')=1-P(A or B)

P(A' and B')=1-0.82

P(A' and B')=0.18

Thus, the probability that a course has NEITHER of these two requirements is 0.18.

3 0
2 years ago
Shannon scores 36 points on 6 questions on her test what is the unit rate for one question?
VLD [36.1K]

Answer:

Uh I think 6

Step-by-step explanation:


7 0
3 years ago
Hey someone pls help the girl out
hichkok12 [17]

Answer:

because one i one is higher than the other, if you look at it

7 0
2 years ago
Read 2 more answers
Other questions:
  • What are even numbers
    9·2 answers
  • Heather and her family are going to the grand opening of a new amusement park. There is a special price on tickets this weekend.
    14·2 answers
  • How do you find the middle term of a perfect square trinomial?
    9·1 answer
  • Rearrange the formula I = √P/R for R.
    11·1 answer
  • Family paid $24,000 as a down payment for a home if this represents 12% of the price of the home, find the price of the home.
    13·2 answers
  • For the sets: A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6} U = {numbers from 0 to 10},
    11·1 answer
  • Is -5/8+3/5 irrational number
    15·1 answer
  • Hey! i’ll give brainliest pls help.
    7·2 answers
  • If g (2) = f (x) + k, what is the value of k?<br> O –12<br> 0 -8<br> O 12
    14·1 answer
  • Find the product: <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B8%7D%20%20%5Ctimes%20%20%5Csqrt%7B8%7D%20" id="TexFo
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!