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Match each event to its probability.
An animal shelter has 48 cats and 12 dogs. If one animal is randomly chosen, what is the probability that a dog is chosen?
There are 4 oranges, 2 bananas, and 6 apples in a bag. If one piece of fruit is randomly chosen, what is the probability that an apple is chosen?
Of 15 pairs of twins born last month, 8 are either both male or both female. If one pair is randomly chosen, what is the probability that the pair chosen consists of a boy and a girl?
A bag contains 3 triangles, 4 squares, 5 pentagons, and 6 hexagons. If one shape is randomly chosen, what is the probability that a hexagon is chosen?
Answer
The final answer: The probability that a dog is chosen is \(\boxed{0.2}\), the probability that an apple is chosen is \(\boxed{0.5}\), the probability that the pair chosen consists of a boy and a girl is \(\boxed{0.4666666666666667}\), and the probability that a hexagon is chosen is \(\boxed{0.3333333333333333}\)
Step 1 ：Calculate the total number of animals in the shelter: \(48 \text{ cats} + 12 \text{ dogs} = 60 \text{ animals}\)
Step 2 ：Calculate the probability of choosing a dog: \(\frac{12 \text{ dogs}}{60 \text{ animals}} = \frac{1}{5} = 0.2\)
Step 3 ：Calculate the total number of pieces of fruit in the bag: \(4 \text{ oranges} + 2 \text{ bananas} + 6 \text{ apples} = 12 \text{ pieces of fruit}\)
Step 4 ：Calculate the probability of choosing an apple: \(\frac{6 \text{ apples}}{12 \text{ pieces of fruit}} = \frac{1}{2} = 0.5\)
Step 5 ：Calculate the total number of pairs of twins born last month: \(15 \text{ pairs of twins}\)
Step 6 ：Calculate the probability of choosing a pair of twins that consists of a boy and a girl: \(\frac{15 \text{ pairs of twins} - 8 \text{ same gender pairs}}{15 \text{ pairs of twins}} = \frac{7}{15} \approx 0.4666666666666667\)
Step 7 ：Calculate the total number of shapes in the bag: \(3 \text{ triangles} + 4 \text{ squares} + 5 \text{ pentagons} + 6 \text{ hexagons} = 18 \text{ shapes}\)
Step 8 ：Calculate the probability of choosing a hexagon: \(\frac{6 \text{ hexagons}}{18 \text{ shapes}} = \frac{1}{3} \approx 0.3333333333333333\)
Step 9 ：The final answer: The probability that a dog is chosen is \(\boxed{0.2}\), the probability that an apple is chosen is \(\boxed{0.5}\), the probability that the pair chosen consists of a boy and a girl is \(\boxed{0.4666666666666667}\), and the probability that a hexagon is chosen is \(\boxed{0.3333333333333333}\)
