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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-13-CON-01
Conditional Probability — Assignment
Chapter: Probability
Topic: Conditional Probability & Multiplication Rule
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.
$P(A\mid B)$ equals:
  • A.$\dfrac{P(A\cap B)}{P(B)}$
  • B.$P(A)P(B)$
  • C.$\dfrac{P(B)}{P(A)}$
  • D.$P(A)+P(B)$
2.
$A,B$ are independent means $P(A\cap B)=$
  • A.$0$
  • B.$P(A)P(B)$
  • C.$P(A)+P(B)$
  • D.$P(A\mid B)$
3.
On a die, $P(>3\mid \text{even})=$
  • A.$\tfrac12$
  • B.$\tfrac23$
  • C.$\tfrac13$
  • D.$\tfrac16$
4.
If $P(A)=0.6,\ P(B\mid A)=0.5$, then $P(A\cap B)=$
  • A.$0.3$
  • B.$1.1$
  • C.$0.11$
  • D.$0.5$
5.
For mutually exclusive events, $P(A\cap B)=$
  • A.$P(A)P(B)$
  • B.$0$
  • C.$1$
  • D.$P(A)+P(B)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $P(A)=0.5,\ P(B)=0.4,\ P(A\cap B)=0.2$, are $A,B$ independent?
7.
Two cards are drawn without replacement. Find $P(\text{both kings})$.
8.
If $P(A)=0.6,\ P(B\mid A)=0.5$, find $P(A\cap B)$.
9.
A die is rolled. Find $P(\text{number}>4\mid \text{number}>2)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A die is rolled. Find $P(\text{even}\mid \text{number}>2)$.
11.
From a bag of $5$ red and $3$ black balls, two are drawn without replacement. Find $P(\text{both red})$.
12.
If $P(A)=0.3,\ P(B)=0.4$ and $A,B$ are independent, find $P(A\cup B)$.
13.
A coin is tossed twice. Find $P(\text{both heads}\mid \text{first is head})$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A family has two children. Find the probability that both are girls given that at least one is a girl.
15.
A can solve a problem with probability $\tfrac12$ and B with $\tfrac13$, independently. Find the probability the problem is solved.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\dfrac{P(A\cap B)}{P(B)}$
  2. (B) $P(A)P(B)$
  3. (B) $\tfrac23$
  4. (A) $0.3$
  5. (B) $0$
Section B — Short Answer (2 marks)
  1. Yes.
  2. $\tfrac{1}{221}$.
  3. $0.3$.
  4. $\tfrac12$.
Section C — Short Answer (3 marks)
  1. $\tfrac12$.
  2. $\tfrac{5}{14}$.
  3. $0.58$.
  4. $\tfrac12$.
Section D — Long Answer (5 marks)
  1. $\tfrac13$.
  2. $\tfrac23$.
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