This problem involves conditional probability.

Let's break it down:

• Probability of passing French 101 (P(A)) = 0.73
• Probability of passing French 102 given that the student passed French 101 (P(B|A)) = 0.93

We are asked to find the probability that a student passes both French 101 and French 102. This is the joint probability, $P(A \cap B)$, and we can calculate it using the formula:

$P(A \cap B) = P(A) \times P(B|A)$

Substituting the values:

$P(A \cap B) = 0.73 \times 0.93 = 0.6789$

So, the probability that a student selected at random will pass both French 101 and French 102 is 0.6789 (or about 67.89%).

Would you like more details or clarifications on any part?

Here are 5 related questions to expand your understanding:

1. What is the probability of passing only French 101 but not French 102?
2. How would the probability change if the conditional probability $P(B|A)$ were different?
3. How can we interpret joint probability in the context of multiple events?
4. What if the probability of passing French 101 were 0.9, how would that affect the result?
5. How does conditional probability differ from independent probability?

Tip: Always verify if the events are independent or dependent before calculating probabilities, as it affects the use of formulas like joint or conditional probability.