contestada

Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products received good reviews, 60% of moderately successful products received good reviews, and 10% of poor products received good reviews. In addition, 40% of products have been highly successful, 35% have been moderately successful, and 25% have been poor products.(A) What is the probability that a product attains a good review?(B) If a new design attains a good review, what is the probability that it will be a highly successful product?(C) If a product does not attain a good review, what is the probability that it will be a highly successful product?

Respuesta :

Answer:

Step-by-step explanation:

The given information can be tabulated as follows.

Success type          High             Moderate              Low            Total

                                 0.40                   0.35                 0.25             1

Good reviews          0.95                    0.60                0.10

Combined prob       0.4*0.95             0.35*0.6          0.25*0.1

                                 0.38                    0.21                  0.025       0.6125

A) the probability that  a product attains a good review

=Prob it it successful and gets good review + Prob it  is moderate successful and gets good review +Prob it it low successful and gets good review

= 0.6125

B) If a new design attains a good review,  the probability that it will be a highly successful product= [tex]\frac{0.38}{0.6125} \\=0.6204[/tex]

C) Prob that does not attain a good review =(0.40*0.05)+0.35(0.4) +(0.25)*0.9

= 0.385

Prob for successful not getting good review = 0.40(0.05) = 0.02

Reqd prob = [tex]\frac{0.02}{0.385} \\=0.05195[/tex]

Using probability concepts, it is found that there is a:

a) 0.615 = 61.5% probability that a product attains a good review.

b) 0.6179 = 61.79% probability that it will be a highly successful product.

c) 0.0519 = 5.19% probability that it will be a highly successful product.

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

Item a:

These following percentages are correspondent to a good review:

  • 95% of 40%(highly successful).
  • 60% of 35%(moderate).
  • 10% of 25(poor).

Hence:

[tex]P(A) = 0.95(0.4) + 0.6(0.35) + 0.1(0.25) = 0.615[/tex]

0.615 = 61.5% probability that a product attains a good review.

Item b:

95% of 40% are successful and attain a good review, hence:

[tex]P(A \cap B) = 0.95(0.4)[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.4)}{0.615} = 0.6179[/tex]

0.6179 = 61.79% probability that it will be a highly successful product.

Item c:

  • 1 - 0.615 = 0.385 do not attain a good review, hence [tex]P(A) = 0.385[/tex].
  • 5% of 40% are successful and attain bad reviews, hence [tex]P(A \cap B) = 0.05(0.4)[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.05(0.4)}{0.385} = 0.0519[/tex]

0.0519 = 5.19% probability that it will be a highly successful product.

A similar problem is given at https://brainly.com/question/14398287

Otras preguntas