QuestionWhether events are independent is not always obvious. Consider a set of basketball free throws by a single player Is the probability of success the same for each free throw? Justify your answer.
Studdy Solution
STEP 1
1. The player attempts multiple free throws.
2. The probability of success for each free throw is not influenced by previous attempts unless stated otherwise.
STEP 2
1. Define independent events.
2. Analyze factors affecting free throw success.
3. Determine if the probability of success is consistent.
STEP 3
Define independent events: Two events are independent if the occurrence of one does not affect the probability of the other occurring.
STEP 4
Consider factors that can affect the probability of success for each free throw: - Player's skill level: A player's overall skill can lead to a consistent probability of success. - Fatigue: As the player takes more shots, fatigue may affect performance. - Pressure: The psychological state of the player can vary with each shot, affecting success. - External conditions: Changes in the environment (e.g., crowd noise) can influence performance.
STEP 5
Determine if the probability of success is consistent:
- If the player's skill level is the only factor considered, and it remains constant, the probability of success for each free throw can be considered the same.
- If other factors such as fatigue, pressure, or external conditions vary, the probability of success may not be the same for each free throw.
Conclusion:
The probability of success for each free throw is not necessarily the same. It depends on whether factors affecting the player's performance remain constant or vary between shots.
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