Question

You've decided you want a plant for your room at the gardening store there are four different kinds of plants to look Fern Cactus and thickness and four different kinds of pots to hold the plants Clay Pot plastic pot metal pipe and wood pot if you randomly pick the plant in the pot what is the probability that you won't get a clay pot or a cactus

Answer 1

9/16

Explanation:

Since it is only 2 sets of 4 coices it would be super easy to write them all out.

Plant 1 Clay

Plant 1 Plastic

Plant 1 Metal

Plant 1 Wood

Plant 2 Clay

Plant 2 Plastic

Plant 2 Metal

Plant 2 Wood

Plant 3 Clay

Plant 3 Plastic

Plant 3 Metal

Plant 3 Wood

Cactus Clay

Cactus Plastic

Cactus Metal

Cactus Wood

16 choics total, take out all with a cactus or clay pot

Plant 1 Plastic

Plant 1 Metal

Plant 1 Wood

Plant 2 Plastic

Plant 2 Metal

Plant 2 Wood

Plant 3 Plastic

Plant 3 Metal

Plant 3 Wood

9 choices left, so probability is 9/16

to do it for any number find the total number of choices again, so 16 then you subtract the number of each category you are excluding. so there were 4 cacti and 4 clay, so subtract 8, to get 8. Then you add back any that had both clay and cacti, which there was one, whn you had a cactus in a clay pot, so add back 1. This gets us 9 again.

This is called the inclusion exclusion principle. Might want to look into this specifically.