Probability is part of the Class 9 Mathematics syllabus for the AISSEE (Sainik School) entrance exam, where Maths carries 200 of 400 marks (50 questions × 4 marks), and for the RMS CET Class 9 paper. AISSEE 2027 is on Sunday, 31 January 2027, with no negative marking.
What Is Probability?
Probability tells us how likely an event is. P(E) = number of favourable outcomes ÷ total number of outcomes.
0 ≤ P(E) ≤ 1. An impossible event has P = 0; a sure event has P = 1.
P(not E) = 1 − P(E).
The sum of probabilities of all outcomes is 1.
Know Your Sample Spaces
Experiment | Outcomes | Total |
|---|---|---|
One coin | H, T | 2 |
Two coins | HH, HT, TH, TT | 4 |
One die | 1, 2, 3, 4, 5, 6 | 6 |
Two dice | (1,1) … (6,6) | 36 |
Deck of cards | 4 suits × 13 cards (26 red, 26 black; 12 face cards) | 52 |
Solved Examples
A coin is tossed. P(head) = 1/2.
A die is rolled. P(even number) = 3/6 = 1/2; P(number greater than 4) = 2/6 = 1/3; P(prime: 2, 3, 5) = 3/6 = 1/2.
Two coins are tossed. P(at least one head) = 3/4 (HH, HT, TH) = 3/4.
A card is drawn from a pack of 52. P(red card) = 26/52 = 1/2; P(king) = 4/52 = 1/13; P(ace of spades) = 1/52.
A bag has 3 red and 5 blue balls. P(red) = 3/8; P(not red) = 1 − 3/8 = 5/8.
Two dice are rolled. P(sum = 7) = 6/36 = 1/6 — (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
Common Mistakes
Counting HT and TH as one outcome — they are different.
Forgetting that 1 is not a prime number.
Giving a probability greater than 1 — that is always wrong.
Practise and Revise
Probability MCQs — 10 questions with answers and explanations
Free AISSEE / RMS Mock Test
Enunciate Academy runs online coaching for Sainik School, RMS, Navodaya and RIMC entrance exams for Class 4 to 9 students across Andhra Pradesh and Telangana. Message us on WhatsApp (94924 44498) to get a free mock test, or see the Spark batch details.
