8. There are one hundred tickets in a box, numbered from 1 to 100. Draw twice, with replacement.
8. There are one hundred tickets in a box, numbered from 1 to 100. Draw twice, with replacement.
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![**Problem 8: Understanding Probability with Replacement**
In this exercise, you have a box containing one hundred tickets, each uniquely numbered from 1 to 100. The task is to draw two tickets, one after the other, with replacement.
**Key Concepts:**
- **Number of Tickets:** 100 tickets, each with a unique number.
- **Drawing with Replacement:** After drawing a ticket, it is replaced back into the box before drawing again. This means the total number of tickets remains the same for each draw.
- **Independent Events:** Each draw is independent of the previous one since the ticket is replaced.
**Exploration:**
When you draw with replacement, the probability of drawing a specific ticket on the first draw is \( \frac{1}{100} \). For the second draw, because the first ticket is replaced, the probability remains \( \frac{1}{100} \) for each ticket.
This concept is crucial in understanding events' independence in probability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab8fb356-539a-49f5-8814-e3cdd7231355%2F83955e1e-0bf3-4c86-9f43-1f6281671e0f%2Fbhdqblk_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 8: Understanding Probability with Replacement**
In this exercise, you have a box containing one hundred tickets, each uniquely numbered from 1 to 100. The task is to draw two tickets, one after the other, with replacement.
**Key Concepts:**
- **Number of Tickets:** 100 tickets, each with a unique number.
- **Drawing with Replacement:** After drawing a ticket, it is replaced back into the box before drawing again. This means the total number of tickets remains the same for each draw.
- **Independent Events:** Each draw is independent of the previous one since the ticket is replaced.
**Exploration:**
When you draw with replacement, the probability of drawing a specific ticket on the first draw is \( \frac{1}{100} \). For the second draw, because the first ticket is replaced, the probability remains \( \frac{1}{100} \) for each ticket.
This concept is crucial in understanding events' independence in probability.
![**a.** What is the probability that you draw first an even number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab8fb356-539a-49f5-8814-e3cdd7231355%2F83955e1e-0bf3-4c86-9f43-1f6281671e0f%2F224e2p_processed.png&w=3840&q=75)
Transcribed Image Text:**a.** What is the probability that you draw first an even number.
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