Ten quick, student-life-style questions covering probability basics, sets, permutations, and combinations. Type your answer or choose, then check.
1) Simple Probability – Weekend Day
A student randomly picks a day of the week for a study group. What is the probability it’s a weekend day? Enter as a fraction (e.g., 1/2).
Weekend = {Sat, Sun} → 2/7. ✅
2) Complement Rule – Driving Test
The chance of passing a driving test is 0.8. What is the probability of failing?
P(fail) = 1 - 0.8 = 0.2. ✅
3) Union of Events – Sports or Music
In a dorm: 60% play sports (S), 30% are in music club (M), and 10% do both. What is P(S ∪ M)?
P(S ∪ M) = 0.6 + 0.3 − 0.1 = 0.8. ✅
4) Intersection – Both Sports and Music
From Q3 data, what is P(S ∩ M)?
Given: 10% → 0.10. ✅
5) Mutually Exclusive – Pet Ownership
25% own a cat (C), 35% own a dog (D), and no one owns both. What is P(C ∪ D)?
Mutually exclusive ⇒ add: 0.25 + 0.35 = 0.60. ✅
6) Independence – Coffee & 8am Class
P(coffee)=0.7, P(attend 8am)=0.5, assume independence. Find P(both).
P = 0.7 × 0.5 = 0.35. ✅
7) Permutations – Podium Places
Five students compete. How many ways to award 1st, 2nd, 3rd (order matters)?
P(5,3)=5×4×3=60. ✅
8) Combinations – Choose Reps
From 4 students, choose 2 representatives (order doesn’t matter). How many ways?
C(4,2)=6. ✅
9) Conditional/Joint – Laptop & Online
40% own laptops; 70% of owners take online courses. Find P(own laptop AND take online).
P = 0.40 × 0.70 = 0.28. ✅
10) Deck of Cards – Red or King
Pick 1 card from a standard 52-card deck. Probability it’s a red card or a king?
Red=26, Kings=4, overlap=2 (red kings). (26+4−2)/52=28/52=7/13. ✅
Quick Formulas
Permutations: P(n,k)=n!/(n−k)! | Combinations: C(n,k)=n!/[k!(n−k)!] | Addition rule: P(A∪B)=P(A)+P(B)−P(A∩B) | Complement: P(A′)=1−P(A)