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You've decided you want a plant for your room. At the gardening store, there are different kinds of plants (tulip, fern, cactus, and ficus) and different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).If you randomly pick the plant and the pot, what is the probability that you won't get a clay pot or a cactus?
Full solution
Q. You've decided you want a plant for your room. At the gardening store, there are different kinds of plants (tulip, fern, cactus, and ficus) and different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).If you randomly pick the plant and the pot, what is the probability that you won't get a clay pot or a cactus?
- Plant-Pot Combinations: There are kinds of plants and kinds of pots, making a total of different combinations.
- Combinations without Clay Pot: To not get a clay pot, there are other pots to choose from for each plant, so plants other pots combinations without a clay pot.
- Combinations without Cactus: To not get a cactus, there are other plants to choose from for each pot, so pots other plants combinations without a cactus.
- Subtracting Overlap: We counted the combinations without a clay pot and without a cactus separately, but we need to subtract the overlap, which is the combinations without a clay pot and a cactus. There are other pots and other plants, so combinations that are neither a clay pot nor a cactus.
- Final Calculation: Now, we add the combinations without a clay pot and without a cactus, then subtract the overlap: . This is incorrect because we double-counted the combinations without a clay pot and without a cactus. We should have only subtracted the overlap once.
