Situation
Learning and trying to understand conditional probability by applying it to a sample set of baseball game statistics.
Data
G (Games) : 190,313
AB (Hitting Attempts) : 680,024
H (Hits) : 205,837
HR (Home Runs) : 16,417
Probabilities
P(H) = H / AB = 0.30269 = 30.37%
P(HR) = HR / H = 0.07976 = 7.98%
Conditional Probability:
P(H and HR) = P(H) * P(HR | H)
P(HR | H) = P(H and HR) / P(H)
Goal
P(HR | H) = ?
Determine the probability of hitting a Home Run, given that a Hit occurred.
Questions
- Not certain how to apply conditional probability to determine the result.
- These seem like dependent events since Home Runs is impacted by the number of Hits, so not sure how that impacts the outcome.
- Does Baye's Theorem need to be applied in this case? If not, in would it be necessary?