Probability Practice Questions
Class 12 · Mathematics · 917 free MCQs with instant results and detailed explanations.
917
Total
438
Easy
340
Medium
139
Hard
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Topics in Probability
Bayes' Theorem
218
Random Variables
311
Conditional Probability
230
Binomial Distribution
158
Sample Questions from Probability
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
A student is selected at random from a class of 30 students, where 18 are girls and 12 are boys. What is the probability that a selected student is a girl given that the student is not a boy?
A.
0.6
B.
0.5
C.
0.4
D.
0.3
Show Answer & Explanation
Correct Answer: A
If we know the student is not a boy, we only consider the girls. Thus, the probability is the number of girls divided by the total number of students who are not boys.
Q2
Easy
In a class of 30 students, 18 are boys and 12 are girls. If one student is selected at random, what is the probability that the student is a boy given that the selected student is not a girl?
A.
0.6
B.
0.9
C.
0.8
D.
0.5
Show Answer & Explanation
Correct Answer: A
Since the selected student cannot be a girl, the probability of selecting a boy is 18 out of 30, which simplifies to 0.6.
Q3
Easy
If two events A and B are independent, how does P(A|B) relate to P(A)?
A.
P(A|B) = P(A)
B.
P(A|B) = P(A) + P(B)
C.
P(A|B) = P(A) × P(B)
D.
P(A|B) = 1 - P(A)
Show Answer & Explanation
Correct Answer: A
For independent events, the occurrence of B does not affect the probability of A.
Q4
Medium
A and B are two independent events where P(A) = 0.4 and P(B) = 0.5. What is the probability of A given B?
A.
0.4
B.
0.2
C.
0.5
D.
0.6
Show Answer & Explanation
Correct Answer: A
Since A and B are independent, P(A|B) = P(A). Therefore, the answer is 0.4.
Q5
Medium
A factory produces 90% of its items correctly. If one item is picked and found to be defective, what is the probability that a randomly selected item is defective given that it is from the factory?
A.
0.1
B.
0.3
C.
0.05
D.
0.2
Show Answer & Explanation
Correct Answer: A
The probability of picking a defective item is simply 1 - 0.9 = 0.1 since a correct item is produced 90% of the time.
Q6
Medium
A box contains 2 defective and 8 non-defective bulbs. If one is selected at random, what is the probability that it is non-defective given that it is not defective?
A.
0.8
B.
0.6
C.
0.5
D.
0.4
Show Answer & Explanation
Correct Answer: A
Since the selected bulb is confirmed to be non-defective, and there are 8 non-defective out of a total of 10, the probability is 8/10 = 0.8.
Q7
Medium
A bag contains 5 white and 5 black balls. What is the probability of picking a black ball given that a white ball has been removed from the bag?
A.
0.5
B.
0.4
C.
0.6
D.
0.3
Show Answer & Explanation
Correct Answer: A
After removing a white ball, there are still 5 black balls out of a total of 9 balls. So, P(Black|White removed) = 5/9 = 0.5.
Q8
Hard
In a city, 70% of the people own a car, and 80% of car owners have insurance. If a person is selected at random, what is the probability that they have insurance given that they own a car?
A.
0.56
B.
0.64
C.
0.72
D.
0.8
Show Answer & Explanation
Correct Answer: D
The conditional probability that a person with a car has insurance is simply the given percentage of car owners who have insurance, which is 80% or 0.8.
Q9
Hard
A student has an 80% chance of passing a test. If he studies, this probability increases to 90%. If he studies, what is the probability he will pass the test?
A.
0.8
B.
0.9
C.
0.72
D.
0.88
Show Answer & Explanation
Correct Answer: B
The probability of passing given that he studies is directly given as 90% or 0.9.
Q10
Hard
In a game, the probability of winning is 0.3. If the player wins, the probability of getting a bonus is 0.4. What is the probability of getting a bonus given that the player wins?
A.
0.1
B.
0.12
C.
0.4
D.
0.5
Show Answer & Explanation
Correct Answer: C
The probability of getting a bonus after winning is directly given as 0.4.
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Probability — Class 12 Mathematics Practice Questions Online
This page contains 917 practice MCQs for the chapter Probability in Class 12 Mathematics. The questions are organized by difficulty — 438 easy, 340 medium, 139 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. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.