Also in 2026 Practice Test B Math, question 39; 2025 Practice Test B Math, question 46.
Question
In a sample of 50 cars at a local dealership, there are 12 red cars and 10 cars with backup cameras. Of the 12 red cars, 4 have backup cameras. If a car is selected at random from the given sample, what is the probability that both of the following are true: the car is not red and does not have a backup camera?
- A
- B
- C
- D
Show the answer
Correct answer: B
Create a chart using the given information and use subtraction to figure out how many cars are not red and do not have a back-up camera:
| Red | Not Red | TOTAL | |
| Back-up Camera | 4 | 6 (10-4) |
10 |
| No back-up Camera | 32 (38-6) |
||
| TOTAL | 12 | 38 (50-12) |
50 |
The probability of selecting a car that meets both conditions from the total of 50 cars at the dealership is .
Question analysis
In a sample of 50 cars, 12 are red, 10 have backup cameras, and 4 of the red cars have cameras. Students find the probability that a randomly chosen car is neither red nor equipped with a camera. It tests compound probability with overlapping groups, and the overlap between red cars and camera cars is what makes it tricky.
- NYS standards
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- Above grade 7 Grade 7 compound probability usually uses a ready-made table or tree. Here students must build the two-way table from words, handle an overlap, and use a "not this and not that" condition, several steps beyond typical work.
- Estimated difficulty
- Hard: combines ideas, needs a plan, and has more than one tempting wrong answer.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Much to keep track of major
- Many steps moderate
- A very close wrong answer moderate
- Complex sentences minor
- Solution
- 4 steps
- Reading level
- Question and choices: about grade 6, 63 words.
- Corrected from the DOE handbook
- A grammar slip in the explanation was corrected.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
This is an overlap problem dressed as probability: the hard part is counting the cars that avoid both features, not the division by 50. A two-way table makes it routine, but students working in their heads often keep only one of the two conditions. The question rewards placing the 4 red cars with cameras in the table before doing any subtraction.
Much to keep track of major Working it out
Three overlapping counts, 12 red, 10 with cameras and 4 that are both, must be sorted into four groups before the wanted one, neither red nor with a camera, can be found. (Sweller, 1988; Carpenter, Just & Shell, 1990)
Many steps moderate Working it out
Find the non-red cars with cameras, 10 − 4 = 6, and the non-red cars, 50 − 12 = 38, subtract to get 32, then simplify 32/50. (Daniel & Embretson, 2010; Enright, Morley & Sheehan, 2002)
A very close wrong answer moderate Choosing the answer
19/25, or 38/50, has the same denominator as the right 16/25 and sits just above it; only removing the 6 non-red cars that have cameras from the 38 separates them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)
Complex sentences minor Understanding the question
The last sentence stacks "both of the following are true", a colon and two negatives, "not red" and "does not have"; untangling it is reading work, not extra math. (Abedi & Lord, 2001; Freedle & Kostin, 1993; Messick, 1989)
Strategy: Draw a two-way table with red and not red across, camera and no camera down, fill in the given counts, and complete the missing cells by subtraction.
Traps
- Misreads the question: Misses or misreads a condition or a word in the question: "at least", "each", "remaining", "not".
- Answers a different question: A choice is right for another quantity: the other unknown, the rest instead of the part, the part instead of the whole.
The wrong answers, classified
A Answers a different question (King et al., 2004; Hegarty, Mayer & Monk, 1995)
Finds the 6 non-red cars with cameras and divides by the 10 camera cars, 6/10 = 3/5, a different probability from the one asked.
C Misreads the question (Hegarty, Mayer & Monk, 1995)
Uses only the 38 cars that are not red, 38/50, and ignores the second condition that the car also lacks a backup camera.
D Misreads the question (Hegarty, Mayer & Monk, 1995)
Counts only the 40 cars without backup cameras, 40/50, dropping the requirement that the car must not be red as well.
What was corrected from the DOE handbook, and why
- Explanation: The handbook says “a car that meet both conditions”; the site says “a car that meets both conditions.”
Worked solution, step by step
Formulas used
- Probability
- P is the probability, the chance that something happens. The top counts the results you want. The bottom counts every possible result. Use it when each result is equally likely, like picking one at random.
Sort out what you know
There are 50 cars. Of these, 12 are red and 10 have backup cameras. Of the red cars, 4 have cameras. You pick one car at random. You need the chance that “both of the following are true”: the car is not red, and it has no camera.
Set up a two-way table
A two-way table sorts each car by two things at once: its color and its camera. Put in the numbers you know.
Red Not red Total Camera 4 ? 10 No camera ? Total 12 ? 50 Fill in the missing numbers
Not red with a camera: cars.
All cars that are not red: cars.
Not red with no camera: cars.
Watch out: the 38 cars that are not red include 6 with cameras. Using 38 gives , choice C. Using all 40 cars with no camera gives , choice D.
Write the probability
Use the probability formula. There are 32 cars you want out of 50 cars in all.
Divide the top and bottom by 2.
So the answer is B, .
Check your answer
Finish the table. Red cars with no camera: . Now add the four inside boxes: . That is every car, so the numbers fit. Also, the cars with no camera are , and too.
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The original DOE question
