Tổ hợp và Xác suất Practice Questions
THPT (Vietnam) · THPT Toán · 143 free MCQs with instant results and detailed explanations.
143
Total
46
Easy
74
Medium
23
Hard
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Sample Questions from Tổ hợp và Xác suất
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Q1
Easy
How many different ways can you arrange the letters in the word 'MATH'?
A.
24
B.
12
C.
16
D.
20
Show Answer & Explanation
Correct Answer: A
The word 'MATH' has 4 distinct letters. The number of arrangements of n distinct objects is given by n!. Therefore, 4! = 4 × 3 × 2 × 1 = 24.
Q2
Easy
If you flip a fair coin three times, what is the probability of getting exactly two heads?
A.
3/8
B.
1/2
C.
1/4
D.
5/8
Show Answer & Explanation
Correct Answer: A
The number of ways to get exactly 2 heads in 3 flips is given by C(3, 2) = 3. The total outcomes when flipping a coin 3 times is 2^3 = 8. Thus, the probability is 3/8.
Q3
Easy
In how many ways can you select 2 fruits from a basket containing 5 different fruits?
A.
10
B.
15
C.
20
D.
25
Show Answer & Explanation
Correct Answer: A
The number of ways to choose 2 fruits from 5 is given by the combination formula C(n, r) = n! / (r!(n-r)!). For this case, C(5, 2) = 5! / (2!(5-2)!) = 10.
Q4
Medium
In how many ways can you arrange the letters in the word 'MATH'?
A.
12
B.
24
C.
16
D.
20
Show Answer & Explanation
Correct Answer: B
The word 'MATH' has 4 distinct letters. The number of arrangements is given by 4! = 24.
Q5
Medium
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that at least one ball is red?
A.
0.75
B.
0.5
C.
0.65
D.
0.85
Show Answer & Explanation
Correct Answer: A
To find the probability of at least one red ball, we can subtract the probability of drawing no red balls (all blue) from 1. P(no red) = (3/8) * (2/7) = 0.107. Therefore, P(at least one red) = 1 - P(no red) = 1 - 0.107 = 0.75.
Q6
Medium
From a group of 8 friends, how many ways can a committee of 3 be formed?
A.
56
B.
70
C.
28
D.
84
Show Answer & Explanation
Correct Answer: A
The number of ways to choose 3 friends from 8 is given by the combination formula C(n, r) = n! / (r!(n-r)!). Here, C(8, 3) = 8! / (3!5!) = 56.
Q7
Medium
What is the probability of rolling a total of 7 with two six-sided dice?
A.
1/6
B.
1/12
C.
5/36
D.
1/9
Show Answer & Explanation
Correct Answer: A
There are 6 combinations to roll a total of 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). The total number of outcomes when rolling two dice is 36. Therefore, the probability is 6/36 = 1/6.
Q8
Hard
In a class of 30 students, 18 students study Mathematics, 15 students study Physics, and 10 students study both subjects. What is the probability that a randomly selected student studies either Mathematics or Physics?
A.
0.4
B.
0.5
C.
0.7
D.
0.8
Show Answer & Explanation
Correct Answer: C
To find the probability of a student studying either Mathematics or Physics, we use the formula: P(M ∪ P) = P(M) + P(P) - P(M ∩ P). Here, P(M) = 18/30, P(P) = 15/30, and P(M ∩ P) = 10/30. Therefore, P(M ∪ P) = (18/30 + 15/30 - 10/30) = 0.7.
Q9
Hard
A bag contains 5 red balls, 3 blue balls, and 2 green balls. If three balls are drawn at random, what is the probability that all three balls are of different colors?
A.
0.2
B.
0.3
C.
0.4
D.
0.5
Show Answer & Explanation
Correct Answer: B
To find the probability that all three balls drawn are of different colors, we first calculate the total ways to choose 3 balls from 10. Then, we calculate the ways to choose 1 ball of each color. The required probability is the ratio of favorable outcomes to total outcomes, which results in 0.3.
Q10
Hard
In a class of 30 students, 18 study Mathematics, 15 study Physics, and 10 study both subjects. How many students study only Mathematics?
A.
8
B.
10
C.
5
D.
6
Show Answer & Explanation
Correct Answer: A
To find the number of students studying only Mathematics, we can use the formula: Only Mathematics = Total Mathematics - Both subjects. Here, Total Mathematics = 18 and Both subjects = 10, so Only Mathematics = 18 - 10 = 8.
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Tổ hợp và Xác suất — THPT (Vietnam) THPT Toán Practice Questions Online
This page contains 143 practice MCQs for the chapter Tổ hợp và Xác suất in THPT (Vietnam) THPT Toán. The questions are organized by difficulty — 46 easy, 74 medium, 23 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.