Simplify 3.3l : 900ml

This is a kind of question that we can solve using the Bayes' Theorem. We have here all the different conditional probabilities we need to solve this problem.

According to that theorem, the probability of a selected product attains a good review is:

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$ (1)

In words, the probability that a selected product attains a <em>good review</em> is an <em>event </em>that depends upon the sum of the conditional probabilities that the product comes from <em>high successful product</em> P(G|H) by the probability that this product is a <em>highly successful product</em> P(H), plus the same about the rest of the probabilities, that is, P(G|M)*P(M) or the probability that the product has a good review coming from a <em>moderately successful</em> product by the probability of being moderately successful, and a good review coming from a poor successful product by the probability of being poor successful or P(G|P)*P(P).

<h3>The probability that a randomly selected product attains a good review</h3>

In this way, the probability that a randomly selected product attains a good review is the result of the formula (1). Where (from the question):

P(G|H) = 95% or 0.95 (probability of receiving a good review being a highly successful product)

P(G|M) = 60% or 0.60 (probability of receiving a good review being a moderately successful product)

P(G|P) = 10% or 0.10 (probability of receiving a good review being a poorly successful product)

P(H) = 40% or 0.40 (probability of being a highly successful product).

P(M) = 35% or 0.35 (probability of being a moderately successful product).

P(P) = 25% or 0.25 (probability of being a poor successful product).

Then,

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$

$\\ P(G) = 0.95*0.40 + 0.60*0.35 + 0.10*0.25$

$\\ P(G) = 0.615\;or\; 61.5\%$

That is, <em>the probability that a randomly selected product attains a good review</em> is 61.5%.

<h3>The probability that a new product attains a good review is a highly successful product</h3>

We are looking here for P(H|G). We can express this probability mathematically as follows (another conditional probability):

$\\ P(H|G) = \frac{P(G|H)*P(H)}{P(G)}$

We can notice that the probability represents a fraction from the probability P(G) already calculated. Then,

$\\ P(H|G) = \frac{0.95*0.40}{0.615}$

$\\ P(H|G) =\frac{0.38}{0.615}$

$\\ P(H|G) =0.618$

Then, the probability of a product that attains a good review is indeed a highly successful product is about 0.618 or 61.8%.

<h3>The probability that a product that <em>does not attain </em>a good review is a moderately successful product</h3>

The probability that a product does not attain a good review is given by a similar formula than (1). However, this probability is the complement of P(G). Mathematically:

$\\ P(NG) = P(NG|H)*P(H) + P(NG|M)*P(M) + P(NG|P)*P(P)$

P(NG|H) = 1 - P(G|H) = 1 - 0.95 = 0.05

P(NG|M) = 1 - P(G|M) = 1 - 0.60 = 0.40

P(NG|P) = 1 - P(G|M) = 1 - 0.10 = 0.90

So

$\\ P(NG) = 0.05*0.40 + 0.40*0.35 + 0.90*0.25$

$\\ P(NG) = 0.385\;or\; 38.5\%$

Which is equal to

P(NG) = 1 - P(G) = 1 - 0.615 = 0.385

Well, having all this information at hand:

$\\ P(M|NG) = \frac{P(NG|M)*P(M)}{P(NG)}$

$\\ P(M|NG) = \frac{0.40*0.35}{0.385}$

$\\ P(M|NG) = \frac{0.14}{0.385}$

$\\ P(M|NG) = 0.363636... \approx 0.364$

Then, the <em>probability that a new product does not attain a good review and it is a moderately successful product is about </em>0.364 or 36.4%.

8 0

2 years ago

Segment YB is x+3 units long and segment BW is 2x-9 units long. The diagonal YW is ___ units long.

Gnom [1K]

Answer:

3x - 6

Step-by-step explanation:

Segment YB = x + 3

Segment BW = 2x - 9

Add the two segments.

x + 3 + 2x - 9

3x - 6

The diagonal YW is 3x - 6 units long.

6 0

2 years ago

Read 2 more answers

At UF, there are always a few days between the end of classes and the beginning of final exams. These days are meant as a study

Natalija [7]

Answer:

This sample is not representative of all UF students, since those who are not local are not considered.

Step-by-step explanation:

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

However, the sample has to be representative

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected Buffalo residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

In this problem, we have that:

They conduct a phone survey (with local numbers selected at random from the student directory) calling people during "dead week". Will this sample be representative of all UF students?

They only call those students with local numbers.

However, in an university, it is expected that there will be a good percentage of non local students.

So this sample is not representative of all UF students, since those who are not local are not considered.

8 0

2 years ago