An actress has a probability of getting offered a job after a try-out of 0.11. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 3 try-outs.
An actress has a probability of getting offered a job after a try-out of 0.11. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 3 try-outs.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Problem Statement:**
An actress has a probability of getting offered a job after a try-out of 0.11. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 3 try-outs.
**Solution Explanation:**
To solve this problem, we need to determine the probability that the actress will not get a job offer in the first 3 try-outs and thus will need to attend more than 3 try-outs.
1. **Probability of Not Getting an Offer in One Try-Out:**
- The probability of not getting a job in a single try-out is \(1 - 0.11 = 0.89\).
2. **Probability of Not Getting an Offer in the First Three Try-Outs:**
- Since the outcomes are independent, we multiply the probabilities of not getting an offer in each of the first three try-outs:
\[
(0.89)^3 = 0.89 \times 0.89 \times 0.89
\]
3. **Calculation:**
- Performing the calculation gives:
\[
(0.89)^3 = 0.704969
\]
Therefore, the probability that she will need to attend more than 3 try-outs is approximately 0.705, or 70.5%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3caf0467-ca0e-4770-b0d8-25bdaac915d0%2F6530084a-f118-4188-9fbf-b3b71025a1af%2F8g0xcnn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
An actress has a probability of getting offered a job after a try-out of 0.11. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent. Find the probability she will need to attend more than 3 try-outs.
**Solution Explanation:**
To solve this problem, we need to determine the probability that the actress will not get a job offer in the first 3 try-outs and thus will need to attend more than 3 try-outs.
1. **Probability of Not Getting an Offer in One Try-Out:**
- The probability of not getting a job in a single try-out is \(1 - 0.11 = 0.89\).
2. **Probability of Not Getting an Offer in the First Three Try-Outs:**
- Since the outcomes are independent, we multiply the probabilities of not getting an offer in each of the first three try-outs:
\[
(0.89)^3 = 0.89 \times 0.89 \times 0.89
\]
3. **Calculation:**
- Performing the calculation gives:
\[
(0.89)^3 = 0.704969
\]
Therefore, the probability that she will need to attend more than 3 try-outs is approximately 0.705, or 70.5%.
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