To find the probability that Molly will pass the statistics course, given her chances of passing with each professor and the distribution of students, we approach it using conditional probability.

Step 1: Define Probabilities and Events

Let:

• $P(\text{S}) = \frac{70}{120} = 0.5833$: Probability that Molly is assigned to Professor S.
• $P(\text{K}) = \frac{50}{120} = 0.4167$: Probability that Molly is assigned to Professor K.

Molly's probability of passing:

• $P(\text{Pass} | \text{S}) = 0.8$: Probability that she passes if she gets Professor S.
• $P(\text{Pass} | \text{K}) = 0.6$: Probability that she passes if she gets Professor K.

Step 2: Use Total Probability Theorem

The total probability that Molly will pass the statistics course, $P(\text{Pass})$, can be calculated by combining the probabilities for each professor with the chance of being assigned to each professor: $P(\text{Pass}) = P(\text{Pass} | \text{S}) \cdot P(\text{S}) + P(\text{Pass} | \text{K}) \cdot P(\text{K})$ Substitute the values: $P(\text{Pass}) = (0.8 \times 0.5833) + (0.6 \times 0.4167)$ Calculating each term:

1. $0.8 \times 0.5833 = 0.46664$
2. $0.6 \times 0.4167 = 0.25002$

So, $P(\text{Pass}) = 0.46664 + 0.25002 = 0.71666$

Final Answer

The probability that Molly will pass the statistics course is approximately 0.717 (or 71.7%).

Would you like a deeper explanation of any step or to discuss related scenarios?

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Here are five follow-up questions to expand your understanding:

1. What if Molly’s probability of passing with Professor K increased to 0.75? How would that affect her overall probability?
2. How would the calculation change if there were an additional professor with a different probability of passing?
3. What is the probability of failing the course based on the given conditions?
4. How would the answer change if the seats were equally distributed between both professors?
5. If Molly could choose her professor, which one should she choose to maximize her chances?

Tip: When working with conditional probabilities and different scenarios, breaking down each step and using the total probability theorem can simplify complex probability calculations.