Question

4.2 theoretical probability. complement. 200 baseball fans in los angeles are asked whether they hate the giants. 156 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
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Explanation:

Step1: Calculate probability of "yes"

The empirical - probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the total number of fans is $n = 200$, and the number of fans who answered "yes" is $m_1=156$. So the probability that a randomly - chosen fan will answer "yes" is $P(\text{yes})=\frac{156}{200}=\frac{39}{50}$.

Step2: Calculate probability of "no"

The number of fans who answered "no" is $m_2=200 - 156 = 44$. Using the empirical - probability formula, the probability that a randomly - chosen fan will answer "no" is $P(\text{no})=\frac{44}{200}=\frac{11}{50}$.

Answer:

The empirical probability that a randomly chosen fan will answer "yes" is $\frac{39}{50}$.
The empirical probability that a randomly chosen fan will answer "no" is $\frac{11}{50}$.