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You decide to play roulette 4 times, each time betting on red. What is the distribution of X, the number of times you win?

Answers

Answer 1

Answer:

Using the concept of binomial probability, the distribution of X which is the number of winning is ;

X ______ 0 ____1 _____ 2___ 3______ 4

P(X):_0.0767_0.2762_0.3729_0.2238_0.0503

Given the parmaters :

Total Number of slots = 38
Number of reds = 18

The probability of winning,p on a single play :

p = (red slots / total slots) = 18/38 = 9/19

Number of plays = 4

Number of winnings = X

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)
q = 1 - 9/19 = 10/19
n = 4

ForX=0:

P(x = 0) = 4C0 × (9/19)^0 × (10/19)⁴ = 0.0767

ForX=1:

P(x = 0) = 4C1 × (9/19)¹ × (10/19)³ = 0.2762

ForX=2:

P(x = 2) = 4C2 × (9/19)² × (10/19)² = 0.3729

ForX=3:

P(x = 3) = 4C3 × (9/19)³ × (10/19)¹ = 0.2238

For X = 4 :

P(x = 4) = 4C4 × (9/19)⁴ × (10/19)^0 = 0.0503

Therefore, the distribution of X in the roulette spin is :

X ____ 0 ____ 1 _____ 2 ______ 3 ______ 4

P(X):_0.0767_0.2762_0.3729_0.2238 _0.0503

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Answer 2

Answer: 1.
If betting on red, 18/38 = 9/19 chance of winning, so 10/19 chance of losing
Chance of winning 4 times: (9/19)^4 = 6561/130321 =~ 5.034%
Chance of winning 3 times: (9/19)^3 * (10/19) * C(4,1) = 29160/130321 =~ 22.3755%
Chance of winning 2 times: (9/19)^2 * (10/19)^2 * C(4,2) = 48600/130321 =~ 37.2925%
Chance of winning 1 time: (9/19) * (10/19)^3 * C(4,3) = 36000/130321 =~ 27.624%
Chance of winning 0 times: (10/39)^4 = 10000/130321 =~ 76.7336%

Related Questions

We play a card game where we receive 13 cards at the beginning out of the deck of 52. we play 50 games one evening. for each of the the following random variable identify the name and parameters of the distribution: a) The number of aces I get in the first game b) The number of games in which I recieve at least one ace during the evening c) The number of games in which all my cards are from the same suit d) The number of spades I receive in 5th game
If EN=16 and BN=20 what is the scale factor of the dilation?
(6)and-The terms of an expression 4x² – 3xy are:(a) 4x and -3xy (b) 4x² and 3xy(c) 4x² and -xy(d) x
Pls help me pls pls il need help i will mark brainliest
Y = -2(x + 1)(x + 4)

I would appreciate if someone could answer this for a brainlist :)

Answers

Answer:

X=40, Y=140, Z=40 because total sum is 360

Answer:

x is 40° because it's same side interior angle

y is 140° because it's a corresponding angle with the 140° angle

z is 40° because it's a corresponding angle with x

A tank contains 22 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water begun draining and let v represent the volume of water in the tank. Write a formula that expresses y in terms of t .

Answers

Answer:

V= 22-2t

Step-by-step explanation:

I guess the alphabet should be v instead of y. So I am working using v

The rate at which water is draining from the tank is 2gallons/hour. This is the rate of water removal from the tank. So after an hour, 2 × 1= 2 gallons would have drained. After 5 hours, 2×5 =10 gallons would have drained

Therefore to obtain the amount of water in gallons that have been removed from the tank, you will multiply the rate by the time in hours after which the draining started.

Amount (gallons) =2×t

The amount of water remaining in the tank will be obtained by subtracting the amount of water drained after some hour (2×t) from the initial amount of water in the tank (22)

Therefore, the amount of water present in the tank (v)= 22-2t or 2(11-t) gallons

Final answer:

The formula to express volume of the water v in terms of time t is v = 22 - 2t, where 22 is the initial volume and 2t represents the rate at which the water is draining.

Explanation:

This problem is a mathematical representation of a real-world scenario using a linear equation. The volume of water v in the tank can be represented in terms of time t through the equation v = 22 - 2t. This equation illustrates the initial volume of water in the tank (22 gallons) and accounts for the constant rate at which the water is draining (2 gallons per hour).

When time t = 0 (meaning no time has passed since the water started draining), the volume of water v = 22 (the initial volume). As time increases, the volume gradually decreases at a rate of 2 gallons per hour, represented by the term -2t.

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The cost of having a package delivered has a base fee of $10.80. Every pound over 5 lbs cost an additional $0.41 per pound. Write an equation that expresses the cost C in terms of w, the total weight in pounds of a package weighing over 5 lbs. a. C = 10.8w + 0.41 c. C = 0.41(w - 5) + 10.8 b. C = 0.41w + 10.8 d. C = 0.41w + 12.85

Answers

Answer:

c. C = 0.41(w - 5) + 10.8

Explanation:

(w - 5) will represent the number of pounds over 5. For example, for a weight of 6 pounds, 6-5 = 1 is the number of pounds over 5.

The cost is $0.41 for each pound over 5, so that cost can be represented by ...

... 0.41(w - 5)

This charge is in addition to the base charge of $10.80, so the total cost will be ...

... C = 0.41(w - 5) + 10.80

5. Taking a cruise is a costly discretionary expense. In a recent year, the top fivecruise lines in the world had this many passengers:
4,133,000 2,369,000 1,295,000 928,000 679,000
Round your answers to the nearest integer.
a. The computations will be easier to work if you view this problem in terms
of thousands of passengers. Represent each number in terms of thousands
of passengers.
b. What is the mean number of passengers for these five cruise lines? (Give
the full number.)
c. What is the range? (Give the full number.)
d. What is the standard deviation? (Give the full number.)

Answers

Final answer:

The numbers in thousands are: 4133, 2369, 1295, 928, 679. The mean is 1881 thousand passengers, the range is 3454 thousand passengers, and the standard deviation is approximately 1218 thousand passengers.

Explanation:

Part A: To represent each number in terms of thousands of passengers, we simplify them as follows: 4,133,000 is 4,133 thousands of passengers, 2,369,000 is 2,369 thousands, 1,295,000 is 1,295 thousands, 928,000 is 928 thousands, and 679,000 is 679 thousands.

Part B: To calculate the mean number of passengers, you would add up all the passenger numbers and then divide by the number of values (5 in this case). This adds up to 9,404,000 passengers or, in terms of thousands, 9,404. Divided by 5, this gives a mean of 1,880,800 passengers, or 1,881 thousands of passengers.

Part C: The range is calculated by subtracting the smallest number from the largest. In this case, that would be 4,133,000 - 679,000 = 3,454,000, which is also 3,454 thousands of passengers.

Part D: Calculating the standard deviation involves multiple steps. First, for each value, subtract the mean and square this result. Then, calculate the mean of these squared differences. Finally, take the square root of this mean. Doing so, the standard deviation is approximate 1,217,982 passengers, or 1,218 thousands of passengers.

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2,4000,000 in standard form

Answers

Answer:

24 million

Step-by-step explanation:

24,000,000 if you put it porperly

The units are, Unit, Tens, Hundreds, Thousand, Ten-Thousand, Hundred-Thousand, Million, Ten million, Hundred million Billion and so on

We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person