Question

A jar 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? A. 23/22. B. 5/22. C. 9/11. D. 4

Answer 1

The answer is  A. 23/22.

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 (there is OR in a sentence), you will use the addition rule. So, let's just add the probability that the object is green and the probability that the object is a cube.
There are in total 22 objects:
7 blue cubes + 4 blue spheres + 5 green cubes + 6 green spheres = 22 objects.
The probability that the object is green is 11/22 (because there are 11 objects
that are green (5 cubes and 6 spheres) of in total 22 objects).
The probability that the object is a cube is 12/22 (because there are 12 objects that are a cube (7 blue and 5 green) of in total 22 objects).

Thus, the probability that the object is green or a cube is:
$\frac{11}{12} + \frac{12}{12} = \frac{11+12}{12} = \frac{23}{12}$