Question

chapter 4.2 homework
score: 43/83 answered: 26/38
question 27
4.2 theoretical probability. complement.
400 baseball fans in st. louis are asked whether they hate the cubs. 368 of them answered \yes\. enter as a fraction.
the empirical probability that a randomly chosen fan will answer \yes\ is
the empirical probability that a randomly chosen fan will answer
o\ is
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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 $\frac{2}{25}$.