To solve the problem, we need to calculate the empirical probability for each animal type. The empirical probability is determined by dividing the number of times an event occurs by the total number of events. In this case, the event is treating a specific type of animal, and the total number of events is the total number of animals treated.
The total number of animals treated is given by the sum of all animals: Total Animals=35+40+20+15=110 \text{Total Animals} = 35 + 40 + 20 + 15 = 110 Total Animals=35+40+20+15=110
The empirical probability that the next animal treated is a rabbit is calculated as: P(Rabbit)=Number of RabbitsTotal Animals=15110≈0.1364 P(\text{Rabbit}) = \frac{\text{Number of Rabbits}}{\text{Total Animals}} = \frac{15}{110} \approx 0.1364 P(Rabbit)=Total AnimalsNumber of Rabbits=11015≈0.1364
The empirical probability that the next animal treated is a bird is calculated as: P(Bird)=Number of BirdsTotal Animals=20110≈0.1818 P(\text{Bird}) = \frac{\text{Number of Birds}}{\text{Total Animals}} = \frac{20}{110} \approx 0.1818 P(Bird)=Total AnimalsNumber of Birds=11020≈0.1818
The empirical probability that the next animal treated is a cat is calculated as: P(Cat)=Number of CatsTotal Animals=40110≈0.3636 P(\text{Cat}) = \frac{\text{Number of Cats}}{\text{Total Animals}} = \frac{40}{110} \approx 0.3636 P(Cat)=Total AnimalsNumber of Cats=11040≈0.3636
The empirical probabilities are:
Thus, the final answers are: P(Rabbit)≈0.1364 \boxed{P(\text{Rabbit}) \approx 0.1364} P(Rabbit)≈0.1364 P(Bird)≈0.1818 \boxed{P(\text{Bird}) \approx 0.1818} P(Bird)≈0.1818 P(Cat)≈0.3636 \boxed{P(\text{Cat}) \approx 0.3636} P(Cat)≈0.3636
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