Probability Practice Questions with Detailed Solutions – Level 1

Probability Practice Quiz Level 1: Coins, Dice, Cards and Balls

This Level 1 set builds the core skill of probability: counting favourable outcomes and comparing them with all equally likely outcomes. It covers coin tosses, die rolls, playing-card draws, coloured balls and simple independent events. Aptitude360 provides a worked solution for every problem, so you can check each counting step.

Topics covered in this basic probability set

• Tossing several coins and counting heads or tails
• Rolling one die or a pair of dice, including sums, products and doublets
• Drawing kings, queens, hearts, spades or face cards from a standard pack
• Picking coloured balls or marbles with and without replacement
• Complement events, such as the chance that rain does not fall
• Independent events with two people solving a problem or hitting a target
• Numbered cards divisible by a given number, and extra weekdays in leap and non-leap years

Key probability formulas for Level 1

• Basic probability (equally likely outcomes): \( P(E)=\dfrac{n(E)}{n(S)} \)
• Complement: \( P(\bar{E})=1-P(E) \)
• Addition rule: \( P(A\cup B)=P(A)+P(B)-P(A\cap B) \)
• Independent events: \( P(A\cap B)=P(A)\times P(B) \)

Revision tips for beginner probability problems

• Write out the full sample space for coins and dice before counting favourable cases.
• In either-or card problems, subtract the overlap, such as the king of hearts, so it is not counted twice.
• When a ball is not put back, reduce the count of the colour drawn and the total by one before the second draw; the counts of the other colours stay unchanged.
• For leap-year problems, list the extra days beyond complete weeks and check which pairs contain the required weekday.

Who should take this Level 1 set

This set suits students starting probability for aptitude tests or school maths. It also works as a quick refresher before moving to the harder levels.