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You've decided you want a plant for your room. At the gardening store, there are 4 different kinds of plants (tulip, fern, cactus, and ficus) and 4 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?

Verified Answer :

WordSpinner

So, there is a 1/4 chance you won't get a clay pot, and a 1/4 chance you won't get a cactus. That means there is 3/4 chance that you will get a clay pot, and a 3/4 chance you'll get a cactus. Just multiply the two. 

The probability that you won't get a clay pot or cactus is 9/16.

fichoh

Using the principle of probability, the probability of not getting a clay pot or a cactus plant is 9/16.

Recall :

  • Probability = required outcome / Total possible outcomes

  • P(getting a clay pot) = 1/4

Hence, P(not getting a clay pot) = 1 - 1/4 = 3/4

  • P(getting a cactus plant) = 1/4

Hence, P(not getting a cactus plant) = 1 - 1/4 = 3/4

Therefore, the probability of not getting a clay pot or a cactus plant :

P(not getting both) = 3/4 × 3/4 = 9/16

Therefore, the probability of not getting a clay pot or a cactus plant is 9/16

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