Question

A focus group study has always been the primary way for ABC Toys Company to gather customers' opinions for marketing strategy. In the past, when a new product was popular in the market, a focus group study had incorrectly indicated that it would be unpopular with a probability of 0.275. When a new product was unpopular, a focus group had incorrectly indicated that it would be popular with a probability of 0.175. Assume that the probability of a new product being popular in the market is 0.60. What is the probability that a new product will be unpopular if a focus group study indicates that it will be unpopular?

Answer 1

Using conditional probability, there is a 0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which:

• P(B|A) is the probability of event B happening, given that A happened.

• $P(A \cap B)$ is the probability of both A and B happening.

• P(A) is the probability of A happening.

For this problem, the events are given as follows:

• Event A: Study indicates that the product is unpopular.

• Event B: Product is unpopular.

The parameters are given as follows:

• P(A) = 0.6 x 0.275 + 0.4 x 0.825 = 0.495.

• $P(A \cap B) = 0.4 \times 0.825 = 0.33$

Hence the conditional probability is:

$P(B|A) = \frac{0.33}{0.495} = 0.6667$

0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.

More can be learned about conditional probability at https://brainly.com/question/14398287

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