Suppose the probability of Ann getting a hit in softball is .314. What is the probability that Ann gets at least one hit in her next 8 attempts?
Suppose the probability of Ann getting a hit in softball is .314. What is the probability that Ann gets at least one hit in her next 8 attempts?
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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![**Text:**
Suppose the probability of Ann getting a hit in softball is .314. What is the probability that Ann gets at least one hit in her next 8 attempts?
**Explanation:**
This problem involves calculating the probability of Ann getting at least one hit in the next 8 attempts given a constant probability of .314 per attempt. This is a classic example of the use of complementary probability. Instead of directly calculating the probability of getting at least one hit, it may be easier to first calculate the probability of not getting any hits in all 8 attempts, and then subtract that from 1.
**Calculations:**
To find the probability of not getting a hit in a single attempt, subtract the probability of a hit from 1:
\[ P(\text{no hit in one attempt}) = 1 - 0.314 = 0.686. \]
To find the probability of not getting a hit in 8 attempts, raise this probability to the power of 8:
\[ P(\text{no hits in 8 attempts}) = 0.686^8. \]
Finally, subtract this result from 1 to find the probability of getting at least one hit:
\[ P(\text{at least one hit in 8 attempts}) = 1 - P(\text{no hits in 8 attempts}). \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f7e488f-dfc3-4cc0-b337-e209f551039c%2Fe0f4d08d-1ba5-4388-aefe-1067ecb64e31%2Fqpxdatn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Text:**
Suppose the probability of Ann getting a hit in softball is .314. What is the probability that Ann gets at least one hit in her next 8 attempts?
**Explanation:**
This problem involves calculating the probability of Ann getting at least one hit in the next 8 attempts given a constant probability of .314 per attempt. This is a classic example of the use of complementary probability. Instead of directly calculating the probability of getting at least one hit, it may be easier to first calculate the probability of not getting any hits in all 8 attempts, and then subtract that from 1.
**Calculations:**
To find the probability of not getting a hit in a single attempt, subtract the probability of a hit from 1:
\[ P(\text{no hit in one attempt}) = 1 - 0.314 = 0.686. \]
To find the probability of not getting a hit in 8 attempts, raise this probability to the power of 8:
\[ P(\text{no hits in 8 attempts}) = 0.686^8. \]
Finally, subtract this result from 1 to find the probability of getting at least one hit:
\[ P(\text{at least one hit in 8 attempts}) = 1 - P(\text{no hits in 8 attempts}). \]
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