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 total number of objects in the jar is 22. There are 18 objects that are either green or cubes, giving a probability of 9/11, which is option C.

Step-by-step explanation:

Calculating the Probability of Selecting Green or a Cube

To find the probability that the selected object is green or a cube, we should first count the total number of objects in the jar. Adding up the numbers, we have 7 blue cubes, 4 blue spheres, 5 green cubes, and 6 green spheres, which gives a total of 22 objects (7 + 4 + 5 + 6 = 22). Then we calculate the number of favorable objects for our event. This includes all green objects and all cubes. We have 5 green cubes, 6 green spheres, 7 blue cubes (since 'or' is inclusive and cubes are counted distinct from color). So, the total number of favorable outcomes is 5 + 6 + 7 = 18. The probability is the number of favorable outcomes divided by the total number of objects, which gives us 18/22. This can be simplified to 9/11, which corresponds to option C.

Answer 2

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:

`(11)/(12) + (12)/(12) = (11+12)/(12) = (23)/(12)`