Final answer:
The probability that Millie picks one dog sticker and one fish sticker in any order is 7/15, determined by using a tree diagram and calculating the outcomes.
Step-by-step explanation:
To determine the probability that Millie chooses one dog sticker and one fish sticker, a tree diagram can be used to represent the possible outcomes. Initially, she has 3 dog stickers and 7 fish stickers, making a total of 10 stickers.
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- If she picks a dog sticker first, the probability is 3/10. After that, there will be 2 dog stickers and 7 fish stickers left, making 9 stickers in total. The probability of then picking a fish sticker is 7/9.
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- Alternatively, if Millie picks a fish sticker first, the probability is 7/10. Then, there would be 3 dog stickers and 6 fish stickers left, making 9 stickers in total. The probability of picking a dog sticker next is 3/9.
The probability of one dog and one fish sticker can be found by adding the probabilities of both sequences:
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- Dog first, then fish: (3/10) × (7/9) = 21/90
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- Fish first, then dog: (7/10) × (3/9) = 21/90
Adding these probabilities together:
21/90 + 21/90 = 42/90
This simplifies to 7/15.
Therefore, the probability that Millie picks one dog sticker and one fish sticker in any order is 7/15.