Question 1174231
Let's break down this problem using probability and Bayes' Theorem.

**Define Events:**

* **S:** The product is successful.
* **F:** The product fails.
* **M:** Market research indicates success.

**Given Probabilities:**

* P(S) = 0.70 (Probability of success)
* P(F) = 0.30 (Probability of failure)
* P(M|S) = 0.90 (Probability of market research indicating success given the product is successful)
* P(M|F) = 0.20 (Probability of market research indicating success given the product fails)

**What We Need to Find:**

* P(M and S) (Probability that market research indicates success AND the product is successful)

**Steps:**

1.  **Use the conditional probability formula:**
    * P(M|S) = P(M and S) / P(S)

2.  **Rearrange the formula to solve for P(M and S):**
    * P(M and S) = P(M|S) * P(S)

3.  **Substitute the given probabilities:**
    * P(M and S) = 0.90 * 0.70

4.  **Calculate the result:**
    * P(M and S) = 0.63

**Therefore, the probability that the market research results indicate a successful market for the product and the product actually is successful is 0.63 or 63%.**