Ajar contains 7 blue cubes,4 blue spheres, 5 green cubes, and 6 green spheres. if you select an object at random, what is the probability that the object is green or a cube?

The answer is 9/11.

The addition rule is used to calculate the probability of one of the events from multiple pathways. If you want that only one of the events happens, you will use the addition rule. So, we need to calculate the probability of  two different events - the one is that the object is green, and the other is that the object is a cube.
1. The probability that the object is green:
There are 22 objects in total (7 blue cubes + 4 blue spheres + 5 green cubes + 6 green spheres = 22 objects).
There are 11 green objects (5 green cubes + 6 green spheres = 11 green objects).
So, there are 11 green objects out of 22 objects. Therefore, the probability that the object is green is 11/22.

2. The probability that the object is the cube:
There are 22 objects in total (7 blue cubes + 4 blue spheres + 5 green cubes + 6 green spheres = 22 objects).
There are 12 cube objects (7 blue cubes + 5 green cubes).
So, there are 12 cube objects out of 22 objects. Therefore, the probability that the object is green is 12/22.

Now, using the addition rule, we could calculate the probability that the object is green or a cube:
11/22 + 12/22 = 23/22
But, we counted 5 green cubes in both events and need to subtract them:
23/22 - 5/22 = 18/22 = 9/11