8. According to a study conducted by the Department of Pediatrics, children who are injured two or more times tend to sustain these injuries during a relatively limited time. If the average number of injuries per year for children is λ = 2, what is the probability that a child will sustain exactly three injuries during the year?

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**Problem Statement: Understanding the Probability of Injuries**

According to a study conducted by the Department of Pediatrics, children who are injured two or more times tend to sustain these injuries during a relatively limited time. If the average number of injuries per year for children is represented by λ = 2, what is the probability that a child will sustain exactly three injuries during the year?

**Guidance:**

This problem involves calculating the probability of a specific number of occurrences (in this case, injuries) given a known average rate, which suggests the use of the Poisson distribution. The Poisson distribution is useful for modeling the number of times an event happens in a fixed interval of time or space. Here, you can apply the Poisson probability formula to determine the likelihood of exactly three injuries occurring.
Transcribed Image Text:**Problem Statement: Understanding the Probability of Injuries** According to a study conducted by the Department of Pediatrics, children who are injured two or more times tend to sustain these injuries during a relatively limited time. If the average number of injuries per year for children is represented by λ = 2, what is the probability that a child will sustain exactly three injuries during the year? **Guidance:** This problem involves calculating the probability of a specific number of occurrences (in this case, injuries) given a known average rate, which suggests the use of the Poisson distribution. The Poisson distribution is useful for modeling the number of times an event happens in a fixed interval of time or space. Here, you can apply the Poisson probability formula to determine the likelihood of exactly three injuries occurring.
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Obtain the probability that a child will sustain exactly three injuries during the year.

The probability that a child will sustain exactly three injuries during the year is obtained below as follows:

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