Worksheets › Class 12 › Probability
Class 12 Probability worksheet
CBSE Mathematics. Conditional probability, independent events, Bayes' theorem, random variables and their mean. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
If P(B) = 3/10 and P(A ∩ B) = 3/20, then P(A | B) is:
- 9/40
- 9/200
- 3/20
- 1/2
Answer
(d) 1/2
P(A ∩ B)/P(B) = (3/20)/(3/10)
- 2.
A and B are independent with P(A) = 9/10 and P(B) = 4/5. Then P(A ∪ B) is:
- 18/25
- 1
- 49/50
- 7/25
Answer
(c) 49/50
P(A) + P(B) − P(A)P(B)
- 3.
Two dice are thrown. The probability that the sum is 4, given that both dice show the same number, is:
- 5/6
- 1/36
- 1/12
- 1/6
Answer
(d) 1/6
6 outcomes have "both dice show the same number"; 1 of them also have "the sum is 4"
Section B · short answer
- 4.
If P(A) = 3/10, P(B) = 3/5 and P(A ∩ B) = 1/4, find P(A | B), P(B | A) and P(A ∪ B).
Answer
P(A | B) = 5/12; P(B | A) = 5/6; P(A ∪ B) = 13/20
P(A | B) = P(A ∩ B)/P(B)
- 5.
A and B are independent events with P(A) = 9/10 and P(B) = 4/5. Find P(A ∩ B), P(A ∪ B) and P(neither A nor B).
Answer
18/25; 49/50; 1/50
P(A′ ∩ B′) = P(A′)P(B′)
Section C · long answer
- 6.
A disease affects 8% of a population. A test detects it in 95% of people who have it, but also gives a positive result for 9% of people who do not. A person tests positive. Find the probability that the person has the disease.
Answer
190/397
Bayes: (2/25 × 19/20) ÷ (2/25 × 19/20 + 23/25 × 9/100)
Fresh sheets for your child
In the app, every Probability sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.