Question

A company plans to launch a new product. They have traditionally had a 60% success rate with the launch of new products. Market research predicts that a positive test market results is 80% of successfully launched products and a positive market result for 30% of failed product launches. A) If a market test result comes back negative, what is the probability that the product will be successfully launched?

Answer 1

Answer:

The probability that the product will be successfully launched given that the market test result comes back negative is 0.30.

Step-by-step explanation:

Denote the events provided as follows:

S = a product is successfully launched

P = positive test market result

The information provided is:

P (S) = 0.60

P (P | S) = 0.80

P (P | S') = 0.30

Then,

P (P' | S) = 1 - P (P | S) = 1 - 0.80 = 0.20

P (P' | S') = 1 - P (P | S') = 1 - 0.30 = 0.70

Compute the probability of positive test market result as follows:

$P(P)=P(P|S)P(S)+P(P|S')P(S')$

         $=(0.80\times 0.60)+(0.30\times 0.40)\\\\=0.48+0.12\\\\=0.60$

The probability of positive test market result is 0.60.

Then the probability of negative test market result is:

P (P') = 1 - P (P)

        = 1 - 0.60

        = 0.40

Compute the probability that the product will be successfully launched given that the market test result comes back negative as follows:

$P(S|P')=\frac{P(P'|S)P(S)}{P(P')}$

             $=\frac{0.20\times 0.60}{0.40}\\\\=0.30$

Thus, the probability that the product will be successfully launched given that the market test result comes back negative is 0.30.