Grade 7 Math Practice Test: Probability and Random Sampling
- Probability and Random Sampling
- 15 questions
- 20 minutes
This test covers the probability scale, theoretical and experimental probability, compound events, simulations, random and biased samples, and using samples to make predictions about a population. Tip: write each probability as favorable outcomes over all possible outcomes before you simplify.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A weather app says the probability of snow tomorrow is 0.05. Which word best describes the chance of snow?
Correct answer: A
Probabilities run from 0 (impossible) to 1 (certain). 0.05 is very close to 0 but not equal to it, so snow is unlikely but still possible.
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Question 2
A bag holds 4 red marbles, 6 green marbles and 5 yellow marbles. One marble is picked at random. What is the probability that it is green?
Correct answer: C
There are 4 + 6 + 5 = 15 marbles and 6 are green, so P(green) = 615 = 25. 23 compares green to the 9 other marbles, and 13 wrongly treats the three colors as equally likely.
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Question 3
A fair number cube has faces numbered 1 to 6. What is the probability of not rolling a 5?
Correct answer: B
Five of the six equally likely outcomes (1, 2, 3, 4, 6) are not 5, so the probability is 56. This is 1 − 16; 16 is the probability of rolling a 5.
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Question 4
Kai flipped a coin 50 times and got heads 31 times. What is the experimental probability of heads from his results?
Correct answer: D
Experimental probability = heads ÷ total flips = 31 ÷ 50 = 0.62. 0.50 is the theoretical probability for a fair coin, and 0.38 is the experimental probability of tails (19 ÷ 50).
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Question 5
A quality inspector tests a random sample of 200 light bulbs from a factory and finds that 6 are defective. Based on this sample, about how many defective bulbs would you expect in a shipment of 5,000 bulbs?
Correct answer: A
The sample rate is 6200 = 0.03, or 3%. Then 0.03 × 5,000 = 150 defective bulbs. 30 uses 6 × 5, and 300 doubles the correct rate.
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Question 6
Rosa will roll a fair number cube 300 times. About how many times should she expect to roll a number greater than 4?
Correct answer: C
Only 5 and 6 are greater than 4, so P(greater than 4) = 26 = 13. Then 13 × 300 = 100. 50 counts only one number, and 200 counts the numbers 4 or less.
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Question 7
Mason flips a coin and then rolls a number cube numbered 1 to 6. How many outcomes are in the sample space?
Correct answer: B
Each of the 2 coin results can be paired with each of the 6 cube results, so there are 2 × 6 = 12 outcomes, such as H1, H2, …, T6. 8 adds the numbers instead of multiplying, and 36 would be the result for two number cubes.
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Question 8
A spinner has three equal sections labeled A, B and C. Lena spins it once and flips a fair coin once. What is the probability that she gets B and heads?
Correct answer: D
There are 3 × 2 = 6 equally likely outcomes (AH, AT, BH, BT, CH, CT), and only BH is wanted, so the probability is 16. This equals 13 × 12; 56 adds the probabilities instead of multiplying them.
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Question 9
Two fair number cubes, each numbered 1 to 6, are rolled. What is the probability that the sum is 7?
Correct answer: A
There are 6 × 6 = 36 outcomes. Six of them have a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1). So P(sum of 7) = 636 = 16. 112 comes from treating the 11 possible sums from 2 to 12 as if they were 12 equally likely results.
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Question 10
The student council wants to know which new lunch option the 800 students at a middle school prefer. Which sample is most likely to represent all the students?
Correct answer: C
A random sample from the whole school gives every student the same chance to be chosen, so it is most likely to represent everyone. The other samples favor certain groups, such as early lunch students, council members or students who choose to answer.
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Question 11
To find the favorite sport of people in her town, Ava surveys fans as they leave a basketball game. Why are her results likely to be biased?
Correct answer: B
A sample is biased when the way it is chosen favors some answers. Fans at a basketball game are not typical of the whole town and will likely overstate how popular basketball is. Asking before the game would not fix this.
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Question 12
A school has 900 students. In a random sample of 60 students, 24 said they ride a bike to school. Based on the sample, about how many students in the whole school ride a bike to school?
Correct answer: D
In the sample, 2460 = 0.4, or 40%, ride a bike. Then 0.4 × 900 = 360 students. 540 is the estimate for students who do not ride a bike (60% of 900).
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Question 13
Four groups of students each took a different random sample of 50 seventh graders and recorded the percent who have a pet. Their results were 40%, 44%, 38% and 42%. Which is the best estimate of the percent of all seventh graders who have a pet?
Correct answer: A
Different random samples give slightly different results, so combining them gives a better estimate: (40 + 44 + 38 + 42) ÷ 4 = 164 ÷ 4 = 41%. 6% is the range of the results, which shows how much they vary, not the estimate itself.
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Question 14
The mean height of the players on Team A is 160 cm, and the mean height on Team B is 172 cm. Both teams have a mean absolute deviation (MAD) of 4 cm. The difference between the means is how many times the MAD?
Correct answer: C
The difference between the means is 172 − 160 = 12 cm, and 12 ÷ 4 = 3. So the means are 3 MADs apart, which shows a clear difference between the teams' heights. 12 is the difference in centimeters, not the number of MADs.
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Question 15
A basketball player makes 70% of her free throws. Jamal wants to simulate her free throws with a random digit generator that gives the digits 0 to 9 with equal chance. Which plan models her shots correctly?
Correct answer: B
The digits 0 to 6 are 7 of the 10 equally likely digits, which matches a 70% chance of making a shot, and 7 to 9 are the 30% misses. Digits 0 to 7 are 8 digits, which models 80%, and even/odd models 50%.
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