Robotics Club: Audit the Test Outcomes

Count outcomes to find compound-event probabilities.

Choose a Robot Build

The club is building a robot that moves objects. For Questions 1–4, a computer randomly selects one of the 12 chassis–gripper combinations. Each combination is equally likely. Write probabilities as fractions.

Distance Each Build Moved an Object (cm)
Chassis	Scoop	Claw	Fork	Clamp
Compact	60	80	90	70
Standard	80	70	100	90
Wide	50	80	70	90

The club needs a build that moved the object at least 80 cm. Count the qualifying combinations, then find the probability that the computer selects one.

Number of qualifying outcomes:
Probability:

Select every outcome in the event “the build moved the object exactly 90 cm.”

A build needs a special mounting plate if it has a compact chassis or a scoop, including builds with both. What is the probability that the selected build needs this plate?

A. 7/12B. 1/12C. 1/2D. 5/12

Compare the event “distance is at least 90 cm” with the event “distance is exactly 80 cm.” Which statement is correct?

A. At least 90 cm is more likely: 4 outcomes versus 3.B. Exactly 80 cm is more likely: 4 outcomes versus 3.C. At least 90 cm is more likely: 5 outcomes versus 2.D. The events are equally likely: 3 outcomes each.

The claw is unavailable for the next build. The computer now selects equally among only the nine combinations using a scoop, fork, or clamp. The recorded distances stay the same.

What is the probability that this build moved the object at least 80 cm?

Assign the Battery Packs

Four distinct battery packs are labeled 1, 2, 3, and 4. The club randomly installs one pack in the front compartment and a different pack in the rear compartment. All 12 ordered assignments below are equally likely. The labels identify packs; they are not charge levels.

Complete Battery Assignment Sample Space
Front pack	Rear pack
1	2
1	3
1	4
2	1
2	3
2	4
3	1
3	2
3	4
4	1
4	2
4	3

For a wiring check, the club wants the rear pack's label to be exactly 1 greater than the front pack's label.

What is the probability of this event?

The club saves an assignment for a balance test when the two labels have a sum of at least 6. Select every qualifying outcome. Each pair is (front pack, rear pack).

What fraction of the full sample space has a front-pack label greater than the rear-pack label?

A. 3/12B. 9/12C. 4/12D. 6/12

What is the probability that both installed packs have even-numbered labels?

10.

The club needs pack 1 installed somewhere in the robot. Which fraction correctly counts favorable assignments out of all possible assignments?

A. 3/12B. 6/12C. 1/4D. 2/12

Check the Sensor Tests

A simulator tests the robot's sensor twice. Each test independently returns Clear (C), Delayed (D), or Missed (M), with equal chances. The nine ordered outcomes below are equally likely. The first letter is the first test result.

Complete Two-Test Sample Space
First result	Second: C	Second: D	Second: M
C	CC	CD	CM
D	DC	DD	DM
M	MC	MD	MM

11.

The robot stops for inspection if at least one of the two tests returns Missed.

What is the probability that the robot stops for inspection?

12.

What is the probability that exactly one of the two test results is Clear?

13.

Which event has probability 2/9?

A. The two tests return matching results.B. Exactly one test returns Missed.C. Both tests return Delayed or both return Missed.D. Neither of the two tests returns Missed.

14.

Imani flags a record if the first result is Clear or the second result is Delayed, including records with both. She counts 3 outcomes in the Clear row and 3 in the Delayed column, then reports a probability of 6/9. Explain the counting error and give the correct probability.