Baseball star David Ortiz-nicknamed "Big Papi"-is known for his ability to deliver hits in high-pressure situations. Here is a two-way table of his hi

Maiclubk 2021-03-12 Answered
Baseball star David Ortiz-nicknamed "Big Papi"-is known for his ability to deliver hits in high-pressure situations. Here is a two-way table of his hits, walks, and outs in all of his regular-season and post-season plate appearances from 1997 through 2014. Choose a plate appearance at random. Are the events "Hit" and "Post-season" independent? Justify your answer.
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unessodopunsep
Answered 2021-03-13 Author has 105 answers

DEFINITIONS Two events are independent, if the probability that one event occurs in no way affects the probability of the other event occurring. Definition conditional probability: P(AB)=P(AB)P(A)=P(AandB)P(A) SOLUTION We note that the table contains information about 8883 at-bats (given in the bottom right corner of the table). Moreover, 2110 of the 8883 at-bats are Hits, because 2110 is mentioned in the row ” Total” and in the column ” Hit” of the table. The probability is the number of favorable outcomes divided by the number of possible outcomes: P(Hit)=#of favorable outcomes#of possible outcomes=211088830.2375=23.75%
Next, we note that 352 of the 8883 at-bats are post-season, because 352 is mentioned in the row ”Post” and in the column ”Total” of the given table. P(Post)=#of favorable outcomes#of possible outcomes=3528883
Next, we note that 87 of the 8883 at-bats are hits in post-season, because 87 is mentioned in the row ”Post” and in the column ”Hit” of the given table. P(HitandPost)=#of favorable outcomes#of possible outcomes=878883 Use the definition of conditional probability: P(HitPost)=P(HitandPost)P(Post)
8788833528883
87352
0.2472
=24.72%
If events A and B are independent, then P(A|B)=P(A) and P(B|A)=P(B)
In this case, we note that P(Hit|Post)=0.2472 is not the same as P(Hit)=0.2375 and thus the two events are not independent.

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