In a certain city district, the need for money to buy drugs is stated as the reason for 73% of all thefts. Find the probability that among the next 5 theft cases reported in this district, (a) exactly 2 resulted from the need for money to buy drugs. (b) at most 3 resulted from the need to buy drugs. (a) Find the probability that among the next 5 theft cases reported in this district, exactly 2 resulted from the need for money to buy drugs. P(X=2)= (Round to three decimal places as needed.) (b) Find the probability that among the next 5 theft cases reported in this district, at most 3 resulted from the need to buy drugs. P(X≤3)= (Round to three decimal places as needed.)

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Author:Amos Gilat
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### Probability in Context of Theft Related to Drug Money

#### Problem Statement:
In a certain city district, the need for money to buy drugs is stated as the reason for 73% of all thefts. We are interested in calculating the probabilities related to the next 5 theft cases reported in this district, specifically:

(a) The probability that exactly 2 of the next 5 theft cases resulted from the need for money to buy drugs.
(b) The probability that at most 3 of the next 5 theft cases resulted from the need to buy drugs.

#### Questions:
1. **Find the probability that among the next 5 theft cases reported in this district, exactly 2 resulted from the need for money to buy drugs.**
   \[
   P(X = 2) = \boxed{\phantom{000}}
   \]
   *(Round to three decimal places as needed.)*

2. **Find the probability that among the next 5 theft cases reported in this district, at most 3 resulted from the need to buy drugs.**
   \[
   P(X \leq 3) = \boxed{\phantom{000}}
   \]
   *(Round to three decimal places as needed.)*
Transcribed Image Text:### Probability in Context of Theft Related to Drug Money #### Problem Statement: In a certain city district, the need for money to buy drugs is stated as the reason for 73% of all thefts. We are interested in calculating the probabilities related to the next 5 theft cases reported in this district, specifically: (a) The probability that exactly 2 of the next 5 theft cases resulted from the need for money to buy drugs. (b) The probability that at most 3 of the next 5 theft cases resulted from the need to buy drugs. #### Questions: 1. **Find the probability that among the next 5 theft cases reported in this district, exactly 2 resulted from the need for money to buy drugs.** \[ P(X = 2) = \boxed{\phantom{000}} \] *(Round to three decimal places as needed.)* 2. **Find the probability that among the next 5 theft cases reported in this district, at most 3 resulted from the need to buy drugs.** \[ P(X \leq 3) = \boxed{\phantom{000}} \] *(Round to three decimal places as needed.)*
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