Final answer:
The probability of randomly selecting a blue object or a cube from the jar is 13/21 after simplifying the fraction.
Step-by-step explanation:
The student is asking about the probability of randomly selecting a blue object or a cube from a jar that contains 17 blue cubes, 4 blue spheres, 5 green cubes, and 16 green spheres.
To find the probability, we add the number of blue objects (cubes and spheres) to the number of green cubes because these represent the favorable outcomes. There are a total of 17 (blue cubes) + 4 (blue spheres) = 21 blue objects. There are also 5 green cubes. We do not add the green spheres since they are neither blue nor cubes.
Now, we have a total of 21 (blue objects) + 5 (green cubes) = 26 favorable outcomes. The total number of objects in the jar is 17 (blue cubes) + 4 (blue spheres) + 5 (green cubes) + 16 (green spheres) = 42. The probability is then calculated by dividing the number of favorable outcomes by the total number of objects:
Probability = Favorable outcomes / Total number of objects = 26/42.
This probability can be simplified by dividing both numerator and denominator by 2, so the simplified probability is 13/21.