Grade 7 Math Practice Test: Compound Events, Tree Diagrams and Sample Spaces
- Compound Events
- 10 questions
- 15 minutes
This test covers listing sample spaces, counting outcomes and finding the probability of compound events. Tip: for independent events, multiply the probabilities; if an item is not replaced, the second probability changes.
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 coin is tossed and a number cube (1-6) is rolled. How many outcomes are in the sample space?
Correct answer: C
Each of the 2 coin results pairs with each of the 6 numbers: 2 × 6 = 12. 8 adds the counts instead of multiplying.
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Question 2
A coin is tossed and a number cube (1-6) is rolled. What is the probability of getting heads and an even number?
Correct answer: C
P(heads) = 12 and P(even) = 36 = 12, so the probability is 12 × 12 = 14. 112 is the chance of one single outcome such as heads and 2.
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Question 3
Spinner A has 3 equal sections: red, blue and green. Spinner B has 4 equal sections numbered 1 to 4. What is the probability of red and a number greater than 2?
Correct answer: D
P(red) = 13 and P(3 or 4) = 24 = 12, so 13 × 12 = 16. 56 adds the two probabilities instead of multiplying them.
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Question 4
A lunch menu has 3 sandwiches, 2 sides and 4 drinks. A meal is one sandwich, one side and one drink. How many different meals are possible?
Correct answer: D
Multiply the choices: 3 × 2 × 4 = 24. 9 adds the numbers of choices.
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Question 5
Two number cubes (1-6) are rolled. What is the probability that the sum is 8?
Correct answer: A
The sums of 8 are (2,6), (3,5), (4,4), (5,3) and (6,2): 5 of the 36 outcomes. 19 = 436 misses one of these pairs, usually (4,4) or a reversed pair.
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Question 6
A fair coin is tossed three times. What is the probability of getting exactly two heads?
Correct answer: C
There are 8 outcomes, and HHT, HTH and THH have exactly two heads, so the probability is 38. 14 counts only two of the three arrangements.
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Question 7
A bag has 4 red and 6 blue marbles. A marble is drawn, put back, and a second marble is drawn. What is the probability that both are red?
Correct answer: B
With replacement, each draw has P(red) = 410 = 25, so 25 × 25 = 425. 215 would be the answer without putting the marble back.
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Question 8
A jar has 3 green and 2 yellow marbles. Two marbles are drawn without putting the first one back. What is the probability that both are green?
Correct answer: A
First draw: 35. Then 2 green are left among 4 marbles: 24. 35 × 24 = 620 = 310. 925 treats the draws as if the marble were replaced.
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Question 9
The forecast gives a 30% chance of rain on each day. Which plan correctly simulates one day using random digits 0-9?
Correct answer: B
Three of the ten equally likely digits give 3 out of 10 = 30%. Four digits would give 40%, and 1 or 2 on a cube gives 26, about 33%.
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Question 10
A fair coin is tossed twice. What is the probability of getting at least one head?
Correct answer: A
The outcomes are HH, HT, TH and TT. Three of the four contain at least one head, so the probability is 34. 14 is the chance of two heads or of no heads.
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