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
larisa [96]
3 years ago
5

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

e that two cans are randomly selected from the 18-pack.
a) Determine the probability that both contain diet soda. P(both diet soda)

b) Determine the probability that both contain regular soda. P(both regular)

c) Would this be unusual?

c) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)
Mathematics
1 answer:
crimeas [40]3 years ago
8 0

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c)  P(X = 2) is unusual, P(X = 0) is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

A number of sucesses x is considered unusually low if P(X \leq x) \leq 0.05 and unusually high if P(X \geq x) \geq 0.05

In this problem, we have that:

Two cans are randomly chosen, so n = 2

Two out of 18 cans are filled with diet coke, so \pi = \frac{2}{18} = 0.11

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that P(X = 2) is unusual, since P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958

There is a 19.58% probability that exactly one is diet and exactly one is regular.

You might be interested in
Find the quotient:<br> a 3 ft 4 in<br> b 3 ft 9 in<br> c 4 ft<br> d 3 ft 8 in
Mekhanik [1.2K]

Answer:

3ft 4in

Step-by-step explanation:

2÷6=3 6÷8=0.75. 2×6=12. 12-6=6 6-2=4 4-1=3 3-1=2

6 0
3 years ago
On Thursday, Emily cycled 88 kilometers in 4 hours. On Friday, she cycled at an average of 3 kph faster. What was her average ra
Lunna [17]
On Thursday she cycled 88 km per hr...for 4 hrs
88/4 = 22 km per hr

On Friday, she cycled 3 km per hr faster
22 + 3 = 25 km per hr <==
7 0
3 years ago
Which point on the graph shows the price of 6 ounces of cheese? Use the formula y=x÷2 to find y when x is 6.
Gwar [14]

Answer: The required point is A(6, 3) in the attached graph.

Step-by-step explanation:  We are to find the point on the given graph that shows the price of 6 ounces of cheese.

The formula to be used is given by

y=x\div 2\\\\\Rightarrow y=\dfrac{x}{2}~~~~~~~~~~~~~~~~(i).

Given that,

when x = 2 then y = 1. That is, price of 2 ounces of cheese is $1.

when x = 7 then y = 3.5. That is, price of 7 ounces of cheese is $3.5.

when x = 14 then y = 7. That is, price of 14 ounces of cheese is $7.

Therefore, these points satisfy the given relation (i).

Hence, if x = 6, then from equation (i), we have

y=\dfrac{x}{2}=\dfrac{6}{2}=3.

Thus, the price of 6 ounces of cheese is &3. This gives that the required point is A(6, 3) on the graph attached below.

8 0
3 years ago
Read 2 more answers
A 60 foot ladder is leaned against the side of a building. The bottom of the ladder is 36feet from the building. How high up the
Natasha2012 [34]

Answer:

24 feet 60-36=24

Step-by-step explanation:

Let me know if this is right.

8 0
3 years ago
A grinding stone completes 175 revolutions before coming to a stop. How many radians did the stone complete
alexandr402 [8]

Answer:

175 * 2 * \pi

350\pi radians

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Is this statistical question? Explain<br> What is the shoe size of seventh-grade students?
    5·1 answer
  • X=y+10 and x=2y+3 <br> solve by substitution <br> needing x and y
    13·2 answers
  • Tyrone had 17,000 to invest. He invested part of that amount at 2.5% annual interest for one year and the other part at 6.5% ann
    15·1 answer
  • Identify the vertex of the function, f(x) = 3(x - 1)2 + 5.
    15·2 answers
  • What is 13/20 as a percent
    13·2 answers
  • Find the compound interest earned by the deposit of $1800 at 6% compounded quarterly for 6 years.
    5·1 answer
  • 9 * 6 * 10 / the power of 3
    11·1 answer
  • How to write 37 in Maya math
    7·1 answer
  • Help me plz snsnsns sn
    9·1 answer
  • Solve this simultaneous equation<br> 4x+3y=18<br> x-3y=7
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!