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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.

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Finger [1]

Answer:28 green and 35 red

Step-by-step explanation:

Given

If there are r red counter and g green counter then

Probability of drawing a green counter is P(g)=\frac{4}{9}

and P(g)=\frac{\text{No of g counter}}{\text{Total no of counter}}

Thus \frac{\text{No of g counter}}{\text{Total no of counter}}=\frac{4}{9}

\frac{g}{g+r}=\frac{4}{9}

\Rightarrow 9g=4g+4r

\Rightarrow 5g=4r\quad \ldots(i)

Also if 4 red and 2 green counter is added the probability of drawing a green counter is

P(g)=\frac{10}{23}=\frac{\text{No of g counter}}{\text{Total no of counter}}

\Rightarrow \frac{10}{23}=\frac{g+2}{g+2+r+4}

\Rightarrow \frac{10}{23}=\frac{g+2}{g+r+6}

\Rightarrow 10g+10r+60=23g+46

\Rightarrow 10r+14=13g\ quad \ldots(ii)

Substitute the value of g in equation (ii)[/tex]

\Rightarrow 10\times \frac{5}{4}g+14=13g

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\Rightarrow g=28

Therefore r=35

Thus there 28 green counter and 35 red counter

6 0
3 years ago
Which is the graph of linear inequality 6x+2y>-10
NemiM [27]
For this case we have the following inequality:
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 The first thing we must do is to graph the linear function:
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 Then, we must evaluate ordered pairs in the following way:
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8 0
3 years ago
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9514 1404 393

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Step-by-step explanation:

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  13x = 156 . . . . . . . . . . . . . . divide by °, subtract 24

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  ∠H = (8x -2)° = (8·12 -2)°

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4 0
2 years ago
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Answer:

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Subtracting $25,307.36 (the value after 3 years) from $27,500 (the value after 2 years) yields the difference:  $2,192.64

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Help please?? <br><br>Answer:
Sveta_85 [38]
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3 years ago
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