For a sales​ promotion, the manufacturer places winning symbols under the caps of 23% of all its soda bottles. If you buy a​ six-pack of​ soda, what is the probability that you win​ something?

Answer:

The probability that you win​ something is 0.7916.

Step-by-step explanation:

Let X denote the number of soda bottles having winning symbols under the caps.

The proportion of soda bottles having winning symbols under the caps is, p = 0.23.

Six-pack of soda are randomly bought.

Every bottle is independent of the others to have the symbols under the caps.

The random variable X follows a binomial distribution with parameters n = 6 and p = 0.23.

Then the chance of winning something implies that at least 1 of the bottles in the six-pack have the symbol under the caps.

Compute the value of P (X ≥ 1) as follows:

[tex]P(X\geq 1)=1-P(X<1)\\\\=1-P(X=0)\\\\=1-{6\choose 0}(0.23)^{0}(1-0.23)^{6-0}\\\\=1-0.2084224\\\\=0.7915776\\\\\approx 0.7916[/tex]

Thus, the probability that you win​ something is 0.7916.

The probability of winning something from buying 6 bottles of the considered soda company is 0.7916 approximately.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

For this case, let we take:
X = the number of bottles out of 6 bottles having winning symbols.

Each bottle have the winning symbol(call it success) or not (call it failure).

Each bottle's result is independent of each other in a random picking (if 23% of the number of bottles manufactured is bigger or equal 6).

Then, we have X pertaining binomial distribution, as:
[tex]X \sim B(n=6, p = 0.23)[/tex]

(since success is a bottle having winning stickers, and as there are only 23% such bottles, so chance of success is 23% = 0.23(in decimal)).

Probability of not winning anything = P(X = 0)

From the probability function of binomial distribution, we get:

[tex]P(X = 0) = \: ^nC_xp^x(1-p)^{n-x} = \: ^6C_0(0.23)^0(1-0.23)^6 \approx 0.2084[/tex]

Thus, we get:

Probability of winning something = 1 - probability of not winning anything.

Probability of winning something ≈ 1- 0.2084 = 0.7916

Thus, the probability of winning something from buying 6 bottles of the considered soda company is 0.7916 approximately.

Learn more about binomial distribution here:

https://brainly.com/question/13609688

Help me pleaseeeeeeeeeeeeeee

A flag measures 150 feet by 75 feet. Find its area​

Evan's favourite hobby is origami. He plans to make 100 paper cranes to hang from the ceiling of his bedroom. Yesterday, he made 28 paper cranes in 4 hours. Today, he made 21 paper cranes at the same rate.
How long did Evan spend making paper cranes today?

Write the equation of the line that is parallel to y = -2x + 4 and passes through (3, 1) in slope-intercept form.​

A car is sold for $18,000. After one year, the value of the car is $9,900. Write an exponential function y to determine the value of
the car after x years if the rate of decrease is the same each year.
y =
Estimate the value of the car after 6 years. Round the answer to the nearest dollar.

An airplane travels 550 miles from North Carolina to Tennessee in 90 minutes. At this rate, how many minutes will it take the airplane to travel 6,600 miles?

Can somebody help me and answer this I’ll give u thanks if ur right here’s the picture

3
3. Write an expression that is equivalent to
5
(3y + 15). (4 points)
O 3
-y + 9
5
03
-y + 15
5
09
5
Y + 9
09
- y + 15
5

Can anyone help me find the value of x of this mid segment triangle?

6x-10y=-8
determine if parallel

What is bigger 1.40 or 1.42

In a recent survey of 288 people, 72 said that their favorite color of car was white. What percent of the people surveyed liked white cars?

The sum of two consecutive integers is 41. What are the two integers?

Graphing rational functions

Which represents a function? Edge 2020.

Six comics are to perform on a single evening. Find the probability

Find the value of 6.8 +9.2

Math help! Answers???

The parallelogram shown bellow has an area of 15 units over 2

• The packages of henna powder cost $12 each and the squeeze
bottles cost $3 each. What is Sushmila's total cost for the supplies?

Can you guys please with me out with the question please

Two math questions


Among all pairs of numbers whose sum is 14​, find a pair whose product is as large as possible. What is the maximum​ product?
The pair of numbers whose sum is 14 and whose product is as large as possible is nothing.
​(Use a comma to separate​ answers.)
The maximum product is nothing.

and

- refer to picture

an integer divided from an integer is an integer

Which statement correctly describes the relationship represented by the graph?
A.
The relationship is linear and proportional.

B.
The relationship is linear and non-proportional.

C.
The relationship is non-linear and proportional.

D.
The relationship is non-linear and non-proportional.

Shannon is paid £1150 a month after deductions.

What is her net annual salary? (A year = 12 months)

Factor using the identity:
a3 + b3 = (a + b)(a? - ab + b2)
Z3+8

Given: AB ∩ CD = O, m∠NOD = x,m∠AON = 44º, m∠BOC = 102º.
Find: x.

A checking account is overdrawn if it has a
negative balance. Marc's account is overdrawn by
$45. What will the balance be after he deposits
$170 and writes a check for $59?

Which graph shows a function whose inverse is also a function?

Please help its important!!
Triangle ABC in the figure above represents the area serviced by a shipping company that plans to build a distribution center at the incenter of the triangle located at point E. A circle is constructed to represent the location of the center. The diameter of the circle is 28 miles. The existing road is perpendicular to the incenter and the company is looking to build 2 more perpendicular roads but connecting the other 2 sides of the triangle. How many more miles of road will be needed?

Select one:
A. 28
B. 34
C. 43
D. 56