Probability Practice Questions with Detailed Solutions – Level 2

Probability Practice Quiz Level 2: Unions, Complements and Draws

Level 2 of the Probability practice series is a medium-difficulty set on overlapping events, complements, multi-ball draws and independent trials. Problems mix coins, dice, card pairs and bags of marbles. Aptitude360 provides a full solution for every question, so you can trace where an overlap or replacement step went wrong.

What this medium-level probability set covers

• Unions of events, such as a face card or a spade, and an even number or a high number
• Numbered cards divisible by one number or another
• Two or three balls drawn together using combinations
• At least one success, using the complement of none
• Independent solvers and shooters, including exactly one success
• Ordered comparisons on two dice and the largest number shown
• Pairs of cards of different suits or ranks drawn without replacement

Key rules and formulas for Level 2 probability

• Addition rule: \( P(A\cup B)=P(A)+P(B)-P(A\cap B) \)
• At least one: \( P(\text{at least one})=1-P(\text{none}) \)
• Two items drawn at random without replacement, both from \( r \) favourable out of \( n \): \( \dfrac{\binom{r}{2}}{\binom{n}{2}} \)
• Exactly one of two independent events: \( P(A)(1-P(B))+(1-P(A))P(B) \)
• Exactly \( k \) successes in \( n \) independent trials, each with the same success probability \( p \): \( \binom{n}{k}p^{k}(1-p)^{n-k} \)

How to prepare for these probability questions

• For divisibility by one number or another, add both counts and subtract multiples of their LCM.
• Use combinations when balls are drawn together and the order does not matter.
• In card questions, sort cards into suits and ranks first, then count the overlap separately.

Who this Level 2 set is for

It suits students who are comfortable with basic probability and want to handle overlapping events and multi-step draws before trying harder problems.