Algebra 2 Practice Test: Probability and Counting
- Probability and Counting
- 10 questions
- 15 minutes
These 10 questions practice counting with permutations and combinations, the addition rule, independent events, drawing without replacement and conditional probability from a table. Ask yourself first whether order matters: if it does, use permutations; if not, use combinations.
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 fair coin is flipped 3 times. What is the probability of getting at least one head?
Correct answer: D
Use the complement: the only outcome with no heads is TTT, with probability (1/2)3 = 18. So P(at least one head) = 1 − 18 = 78.
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Question 2
In how many ways can a 3-person committee be chosen from 8 people?
Correct answer: A
Order does not matter in a committee, so use combinations: C(8, 3) = 8 · 7 · 63 · 2 · 1 = 56. The value 336 counts ordered choices.
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Question 3
A club with 10 members elects a president, a vice president and a secretary. No person can hold two offices. How many different results are possible?
Correct answer: B
The offices are different, so order matters: P(10, 3) = 10 · 9 · 8 = 720. The combination C(10, 3) = 120 ignores who gets which office.
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Question 4
Two fair six-sided dice are rolled. What is the probability that the sum is 8?
Correct answer: A
The pairs (2, 6), (3, 5), (4, 4), (5, 3) and (6, 2) give a sum of 8, so there are 5 of the 36 equally likely outcomes.
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Question 5
A bag holds 4 red and 6 blue marbles. Two marbles are drawn one after the other without replacement. What is the probability that both are red?
Correct answer: B
P = 410 · 39 = 1290 = 215. Using 410 twice, as if the first marble were put back, gives 425.
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Question 6
For two events, P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. What is P(A or B)?
Correct answer: C
Addition rule: P(A or B) = 0.5 + 0.4 − 0.2 = 0.7. Simply adding gives 0.9, which counts the overlap twice.
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Question 7
Events A and B are independent, with P(A) = 0.3 and P(B) = 0.6. What is P(A and B)?
Correct answer: A
For independent events, P(A and B) = P(A) · P(B) = 0.3 · 0.6 = 0.18. Adding the probabilities gives 0.9, which is the wrong rule.
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Question 8
Plays a sport No sport Total Grade 10 30 20 50 Grade 11 18 32 50 Total 48 52 100 A student who plays a sport is chosen at random. What is the probability that the student is in Grade 11?
Correct answer: B
The condition limits the group to the 48 sport players, and 18 of them are in Grade 11: 1848 = 38. 1850 = 925 is P(sport | Grade 11), the reverse condition.
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Question 9
How many different arrangements of the letters in the word LEVEL are there?
Correct answer: C
LEVEL has 5 letters with L repeated twice and E repeated twice, so the count is 5!2! · 2! = 1204 = 30. Dividing by only one 2! gives 60.
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Question 10
A lock code uses 4 digits from 0 to 9, and no digit may be repeated. How many codes are possible?
Correct answer: D
Order matters and digits cannot repeat: 10 · 9 · 8 · 7 = 5,040. 10,000 allows repeats, and 210 = C(10, 4) ignores order.
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