← Back to topic
Vidaara.orgClass 11 · Mathematics
CodeVID-M11-14-ADD-01
Addition Theorem & Problems — Assignment
Chapter: Probability
Topic: Addition Theorem and Problems
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$P(A\cup B)=$
  • A.$P(A)+P(B)$
  • B.$P(A)+P(B)-P(A\cap B)$
  • C.$P(A)P(B)$
  • D.$P(A)-P(B)$
2.
For mutually exclusive events, $P(A\cap B)=$
  • A.$1$
  • B.$0$
  • C.$P(A)P(B)$
  • D.$P(A)+P(B)$
3.
If $A,B$ are mutually exclusive, $P(A\cup B)=$
  • A.$P(A)P(B)$
  • B.$P(A)+P(B)$
  • C.$0$
  • D.$1$
4.
If $P(A)=0.5,P(B)=0.4,P(A\cap B)=0.2$, then $P(A\cup B)=$
  • A.$0.9$
  • B.$0.7$
  • C.$0.1$
  • D.$1.1$
5.
$P(A\cap B)=0$ means events are:
  • A.independent
  • B.mutually exclusive
  • C.equal
  • D.sure
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
$P(A)=0.3,\ P(B)=0.5$, mutually exclusive. Find $P(A\cup B)$.
7.
$P(A)=0.6,\ P(B)=0.5,\ P(A\cap B)=0.2$. Find $P(A\cup B)$.
8.
$P(A\cup B)=0.7,\ P(A)=0.4,\ P(B)=0.5$. Find $P(A\cap B)$.
9.
A die is rolled. Find $P(\text{even or} >4)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A card is drawn from $52$. Find $P(\text{king or queen})$.
11.
A die is rolled. Find $P(\text{even or prime})$.
12.
$P(A)=0.25,\ P(B)=0.5,\ P(A\cap B)=0.14$. Find $P(\text{neither } A \text{ nor } B)$.
13.
A card is drawn from $52$. Find $P(\text{red or king})$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In a class, $P(\text{pass Maths})=0.6,\ P(\text{pass English})=0.7,\ P(\text{pass both})=0.5$. Find the probability of passing at least one subject and of passing neither.
15.
Two dice are thrown. Find the probability that the sum is a multiple of $3$ or a multiple of $4$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $P(A)+P(B)-P(A\cap B)$
  2. (B) $0$
  3. (B) $P(A)+P(B)$
  4. (B) $0.7$
  5. (B) mutually exclusive
Section B — Short Answer (2 marks)
  1. $0.8$.
  2. $0.9$.
  3. $0.2$.
  4. $\tfrac23$.
Section C — Short Answer (3 marks)
  1. $\tfrac{2}{13}$.
  2. $\tfrac56$.
  3. $0.39$.
  4. $\tfrac{7}{13}$.
Section D — Long Answer (5 marks)
  1. At least one $=0.8$; neither $=0.2$.
  2. $\tfrac59$.
Generated by Vidaara.org · Assignment VID-M11-14-ADD-01 · vidaara.org