chapter 4.2 homework\nscore: 43/83 answered: 26/38\nquestion 27\n4.2 theoretical probability…
chapter 4.2 homework\nscore: 43/83 answered: 26/38\nquestion 27\n4.2 theoretical probability. complement.\n400 baseball fans in st. louis are asked whether they hate the cubs. 368 of them answered \yes\. enter as a fraction.\nthe empirical probability that a randomly chosen fan will answer \yes\ is \nthe empirical probability that a randomly chosen fan will answer \no\ is \nquestion help: message instructor
Answer
Explanation:
Step1: Recall probability formula
The formula for empirical probability is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.
Step2: Calculate probability of "yes"
The total number of fans is $n = 400$, and the number of fans who answered "yes" is $m_1=368$. So the empirical - probability that a randomly chosen fan will answer "yes" is $P(\text{yes})=\frac{368}{400}=\frac{46}{50}=\frac{23}{25}$.
Step3: Calculate probability of "no"
The number of fans who answered "no" is $m_2=400 - 368=32$. So the empirical - probability that a randomly chosen fan will answer "no" is $P(\text{no})=\frac{32}{400}=\frac{4}{50}=\frac{2}{25}$.
Answer:
The empirical probability that a randomly chosen fan will answer "yes" is $\frac{23}{25}$. The empirical probability that a randomly chosen fan will answer "no" is $\frac{2}{25}$.