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?

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:

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:

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