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Chapter 11: Problem 15

Work each problem.A baseball player with a batting average of .300 comes to bat. What are the odds in favor of the ball player getting a hit?

Short Answer

Expert verified
The odds in favor of the player getting a hit are 3:7.

Step by step solution

01

- Understand Batting Average

The batting average given is .300. This means the player gets a hit 30% of the time.
02

- Convert Percentage to Probability

Convert the batting average to a probability. The probability of getting a hit is 0.300.
03

- Calculate Probability of Not Getting a Hit

The probability of not getting a hit is the complement of getting a hit, which is 1 - 0.300 = 0.700.
04

- Calculate the Odds in Favor

The odds in favor of getting a hit are the ratio of the probability of getting a hit to the probability of not getting a hit. Therefore, the odds in favor are \(\frac{0.300}{0.700}\), which simplifies to 3:7.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

batting average
A batting average is a common statistic used in baseball. It measures a player's hitting performance. The batting average is calculated by dividing the number of hits by the number of at-bats. For example, if a player has 30 hits out of 100 at-bats, their batting average is 0.300. This means the player gets a hit 30% of the time. A higher batting average indicates better performance at the plate.
probability
Probability is a measure of how likely an event is to occur. It ranges from 0 to 1. A probability of 0 means the event is impossible, while a probability of 1 means it is certain. In our example, the player's probability of getting a hit is 0.300. This can also be written as 30%. Understanding probability helps in predicting outcomes. For example, if the player comes to bat 10 times, they are likely to get a hit in about 3 of those at-bats.
complementary events
Complementary events are pairs of events where one event occurs if and only if the other does not. For instance, if Event A is getting a hit, the complementary event, Event B, is not getting a hit. The sum of the probabilities of complementary events always equals 1. In our example, the probability of not getting a hit is 1 minus the probability of getting a hit. Thus, it is 1 - 0.300 = 0.700, or 70%. Identifying complementary events is important for understanding all possible outcomes in a scenario.
odds ratio
The odds ratio is a way of comparing the probabilities of two complementary events. It is the ratio of the probability of one event to its complement. In our batting example, we compare the probability of getting a hit (0.300) to the probability of not getting a hit (0.700). This gives us an odds ratio of 0.300/0.700. Simplifying, we get 3:7. This means that for every 7 times the player does not get a hit, they are likely to get a hit 3 times. The odds ratio provides a different perspective than probability, giving a clearer comparison of how often one event happens compared to its complement.

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Most popular questions from this chapter

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