Final answer:
Questions relate to probability of selecting a particular cave, the likelihood of specific path choices, and determining vector displacement in given scenarios. Methods include calculating probabilities, conditional probabilities, and vector components using trigonometry.
Step-by-step explanation:
The questions at hand involve applying the principles of probability and vector displacement to solve problems related to different scenarios. Since specific numerical data or diagrams are not provided, we'll use general explanations for how to approach such problems.
Probability Concepts
For the probability questions:
- Probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
- Conditional probability is the probability of an event occurring given that another event has already occurred, which is represented by P(A|B) and calculated using the formula P(A and B) / P(B).
- The probability of either A or B occurring (inclusive) is P(A) + P(B) - P(A and B).
Vector Displacement
When it comes to vector displacement:
- Displacement is a vector quantity representing the shortest path between the start and end points.
- The total displacement can be found by using trigonometry if the path consists of straight line segments making specific angles with a reference direction.
- Components of displacement can be calculated using sine and cosine functions for the given angles.