Question 1171673
To solve this problem, we'll use Bayes' Theorem. Here's how we break it down:

**1. Define the Events:**

* H: High demand
* A: Average demand
* L: Low demand
* F: Favorable reception (14 out of 20 employees)

**2. Given Probabilities:**

* P(H) = 0.30 (Prior probability of high demand)
* P(A) = 0.50 (Prior probability of average demand)
* P(L) = 0.20 (Prior probability of low demand)
* P(F|H) = 0.80 (Probability of favorable reception given high demand)
* P(F|A) = 0.55 (Probability of favorable reception given average demand)
* P(F|L) = 0.30 (Probability of favorable reception given low demand)

**3. Calculate the Marginal Probability of Favorable Reception (P(F)):**

* P(F) = P(F|H)P(H) + P(F|A)P(A) + P(F|L)P(L)
* P(F) = (0.80 * 0.30) + (0.55 * 0.50) + (0.30 * 0.20)
* P(F) = 0.24 + 0.275 + 0.06
* P(F) = 0.575

**4. Apply Bayes' Theorem to Find P(H|F):**

* P(H|F) = [P(F|H) * P(H)] / P(F)
* P(H|F) = (0.80 * 0.30) / 0.575
* P(H|F) = 0.24 / 0.575
* P(H|F) ≈ 0.41739

**5. Round to Two Decimal Places:**

* P(H|F) ≈ 0.42

**Therefore, the probability of actual high demand given a favorable reception is approximately 0.42.**