Probability Basics Notes for SSC Statistics

Probability measures how likely an event is. Its value lies between 0 (impossible) and 1 (sure). SSC statistics questions use coins, dice and cards, along with the addition and multiplication rules.

Basic Formula

• P(A) = number of favourable outcomes / total number of outcomes.
• 0 ≤ P(A) ≤ 1, and P(not A) = 1 − P(A).
• Probability of an impossible event is 0 and of a sure event is 1.
• Sum of probabilities of all outcomes of an experiment = 1.

Rules

Standard Sample Spaces

• One coin: 2 outcomes. Two coins: 4 outcomes. Three coins: 8 outcomes.
• One die: 6 outcomes. Two dice: 36 outcomes. The sum 7 can occur in 6 ways.
• A pack of cards has 52 cards: 4 suits of 13, 4 kings, 4 aces, 12 face cards, 26 red and 26 black.

Solved Example

Two coins are tossed. P(at least one head) = 1 − P(no head) = 1 − 1/4 = 3/4.

Quick Tips

• Use the complement rule (1 − P) when "at least one" appears.
• Draw the sample space for small experiments.
• Check whether events are independent or mutually exclusive before choosing the rule.
• Remember the structure of a deck of cards.

Quick Revision Points

• P(A) = favourable / total.
• Probability is always between 0 and 1.
• Independent events: multiply the probabilities.
• Exclusive events: add the probabilities.
• P(not A) = 1 − P(A).
• Two dice give 36 outcomes.

Practice Questions With Answers

1. What is the probability of getting a head in one toss of a coin?
   Answer: 1/2
2. Two dice are thrown. What is the probability that the sum is 7?
   Answer: 1/6
3. What is the probability of drawing a king from a pack of 52 cards?
   Answer: 1/13
4. P(A) = 0.3 and P(B) = 0.4 are independent. Find P(A and B).
   Answer: 0.12
5. A and B are mutually exclusive with P(A) = 0.2 and P(B) = 0.5. Find P(A or B).
   Answer: 0.7
6. If P(A) = 0.35, find P(not A).
   Answer: 0.65
7. Two coins are tossed. Find P(at least one head).
   Answer: 3/4
8. What is the probability of a sure event?
   Answer: 1

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Statistics notes page.

Frequently Asked Questions

What is probability?

A number between 0 and 1 that measures the chance of an event.

What are mutually exclusive events?

Events that cannot happen at the same time.

What are independent events?

Events where the result of one does not change the probability of the other.

What is the complement rule?

P(not A) = 1 − P(A).

How many outcomes are there when two dice are thrown?

36.

How many cards are there in a pack?

52 (26 red and 26 black).

What is conditional probability?

The probability of A given that B has occurred.

What is the addition theorem?

P(A or B) = P(A) + P(B) − P(A and B).

What is the probability of an impossible event?

Zero.

How can I practise?

Solve 10 coin, dice and card problems every day.