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Vidaara.orgClass 8 · Mathematics
CodeVID-M08-19-GAM-01
Probability Games & Applications - Assignment
Chapter: Probability
Topic: Probability Games and Applications
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.
A game is fair if all players have:
  • A.different chances
  • B.an equal chance
  • C.no chance
  • D.one turn
2.
Rolling two dice gives how many outcomes?
  • A.$12$
  • B.$36$
  • C.$6$
  • D.$18$
3.
Tossing two coins gives how many outcomes?
  • A.$2$
  • B.$3$
  • C.$4$
  • D.$6$
4.
$P(\text{two heads with two coins})=$
  • A.$\tfrac12$
  • B.$\tfrac14$
  • C.$\tfrac13$
  • D.$1$
5.
$P(\text{sum of }7\text{ with two dice})=$
  • A.$\tfrac{1}{12}$
  • B.$\tfrac16$
  • C.$\tfrac15$
  • D.$\tfrac{1}{36}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
How many outcomes when two coins are tossed?
7.
How many outcomes when two dice are rolled?
8.
Find $P(\text{two heads})$ when tossing two coins.
9.
Is a coin toss a fair way to decide?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Two coins are tossed. Find $P(\text{at least one head})$.
11.
Two dice are rolled. Find $P(\text{a sum of }7)$.
12.
Two dice are rolled. Find $P(\text{a double})$.
13.
Two coins are tossed. Find $P(\text{no heads})$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Two dice are rolled. Find $P(\text{a sum of }8)$ and $P(\text{a sum} > 10)$.
15.
In a game you win by tossing two coins and getting two heads. Find $P(\text{win})$ and $P(\text{lose})$, and state whether the game is fair on a single try.

Answer Key

Section A — Multiple Choice Questions
  1. (B) an equal chance
  2. (B) $36$
  3. (C) $4$
  4. (B) $\tfrac14$
  5. (B) $\tfrac16$
Section B — Short Answer (2 marks)
  1. $4$.
  2. $36$.
  3. $\tfrac14$.
  4. Yes.
Section C — Short Answer (3 marks)
  1. $\tfrac34$.
  2. $\tfrac16$.
  3. $\tfrac16$.
  4. $\tfrac14$.
Section D — Long Answer (5 marks)
  1. $\tfrac{5}{36}$ and $\tfrac{1}{12}$.
  2. $P(\text{win})=\tfrac14$, $P(\text{lose})=\tfrac34$; not fair (winning is much less likely than losing).
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