### Probability of Winning the Lottery - Example Problem**Problem Statement:**Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 42 and, in a separate drawing, you must also select the correct single number between 1 and 57. Find the probability of winning the jackpot.**Question:**The probability of winning the jackpot is ____.(Type an integer or simplified fraction.)**User Interface:**- There is an input box where you can enter your answer.- Below the input box, there is a “Check Answer” button to submit your response.- The interface also provides navigation buttons to other questions (not shown in this context).**Status:**- Current score: 0 of 2 points.- Homework score: 57.33%, with 28.67 out of 50 points earned.- Currently on question 5 out of a total of 25 questions in this section.**Instructions:**Enter your answer in the answer box and then click "Check Answer" to see if you are correct. Make sure to type your answer as an integer or a simplified fraction.**Solution Explanation:**To solve this, calculate the probability of each part of the lottery drawing separately and then combine them.1. **Selecting the two correct numbers between 1 and 42:** - The total number of ways to choose 2 numbers out of 42 is calculated using combinations: \[ \binom{42}{2} = \frac{42!}{2!(42-2)!} = \frac{42 \times 41}{2 \times 1} = 861 \] - So, the probability of selecting the two correct numbers is: \[ P_1 = \frac{1}{861} \]2. **Selecting the correct single number between 1 and 57:** - The number of ways to choose 1 number out of 57 is 57: \[ P_2 = \frac{1}{57} \]3. **Combined probability of both independent events happening:** - Since the two events are independent, the combined probability is: \[ P = P_1 \times P_2 = \frac{1}{861} \times \frac{1}{57} = \frac{1}{49077} \]Thus,

We have to find probability for given data..

Score: 0 of 2 pts 5 of 25 (16 complete) v HW Score: 57.33%, 28.67 of 50 p 4.4.17 Question Help ▼ Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 42 and, in a separate drawing, you must also select the correct single number between 1 and 57. Find the probability of winning the jackpot. The probability of winning the jackpot is. (Type an integer or simplified fraction.) Enter your answer in the answer box and then click Check Answer. Check Answer Clear All All parts showing MacBook

Score: 0 of 2 pts 5 of 25 (16 complete) v HW Score: 57.33%, 28.67 of 50 p 4.4.17 Question Help ▼ Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 42 and, in a separate drawing, you must also select the correct single number between 1 and 57. Find the probability of winning the jackpot. The probability of winning the jackpot is. (Type an integer or simplified fraction.) Enter your answer in the answer box and then click Check Answer. Check Answer Clear All All parts showing MacBook

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Probability of Winning the Lottery - Example Problem

**Problem Statement:**
Winning the jackpot in a particular lottery requires that you select the correct two numbers between 1 and 42 and, in a separate drawing, you must also select the correct single number between 1 and 57. Find the probability of winning the jackpot.

**Question:**
The probability of winning the jackpot is ____.
(Type an integer or simplified fraction.)

**User Interface:**
- There is an input box where you can enter your answer.
- Below the input box, there is a “Check Answer” button to submit your response.
- The interface also provides navigation buttons to other questions (not shown in this context).

**Status:**
- Current score: 0 of 2 points.
- Homework score: 57.33%, with 28.67 out of 50 points earned.
- Currently on question 5 out of a total of 25 questions in this section.

**Instructions:**
Enter your answer in the answer box and then click "Check Answer" to see if you are correct. Make sure to type your answer as an integer or a simplified fraction.

**Solution Explanation:**
To solve this, calculate the probability of each part of the lottery drawing separately and then combine them.

1. **Selecting the two correct numbers between 1 and 42:**
- The total number of ways to choose 2 numbers out of 42 is calculated using combinations:
\[
\binom{42}{2} = \frac{42!}{2!(42-2)!} = \frac{42 \times 41}{2 \times 1} = 861
\]
- So, the probability of selecting the two correct numbers is:
\[
P_1 = \frac{1}{861}
\]

2. **Selecting the correct single number between 1 and 57:**
- The number of ways to choose 1 number out of 57 is 57:
\[
P_2 = \frac{1}{57}
\]

3. **Combined probability of both independent events happening:**
- Since the two events are independent, the combined probability is:
\[
P = P_1 \times P_2 = \frac{1}{861} \times \frac{1}{57} = \frac{1}{49077}
\]

Thus,

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