Probability
Practice problems for Probability
- Angle Between Clock Hands at 12:15
- At Least 4 Heads in 7 Coin Flips
- Birthday Day-of-Week Coincidence for Three People
- Chicken Egg Production Rate
- Drawing Two Cards of the Same Color
- Eight-Letter Word with Letter Values Summing Below 50
- Expected Flips to Get Two Heads
- Expected Flips Until First Heads on Fair Coin
- Half Heads
- Order Statistics: Probability the Maximum is Below a Threshold
- Probability All Three Coin Flips Match
- Probability of Even Heads in N Coin Flips
- Probability of Odd Number of Heads in Fair Coin Tosses
- Probability of Sum 10 with Three Dice
- Probability Two Dice Sum to Seven
- Two Children: Younger is a Girl
- Card Deck Comparison: Probability of Two Red Cards
- Bayesian Analysis of Negative Cancer Test
- Bayesian Inference with Unreliable Witnesses
- Bayesian Urn Selection After Drawing $10 Chip
- Best-of-Three Tennis Match: Two Sets vs Three Sets
- Calculate Group Average Salary While Keeping Individual Salaries Private
- Calculate Test Score with Penalty for Wrong Answers
- Circular Seating in Birthday Order
- Coin Flip Competition: 17 vs 16 Coins
- Coin Guessing Game: Probability of Winning
- Conditional Card Drawing: Heart Probability
- Coupon Collector Problem: Expected Die Rolls to See All Faces
- Creating Fair Coin from Biased Coin
- Die Roll with Optional Reroll
- Die Rolling Game: Maximize Sum Without Busting
- Distribution of Sum of Two Uniform Random Variables
- Drawing Balls Until One Color Exhausted
- Evaluate Betting Strategy for HHH with Given Odds
- Even Sum from Three Random Primes
- Exact Probability of 50 Heads in 100 Fair Coin Flips
- Expected Card Value in Standard Deck
- Expected Flips for Three Consecutive Heads
- Expected Maximum of Two Dice
- Expected Samples Until Sum Exceeds One
- Expected Sum Given At Least One Six
- Expected Tosses for N Consecutive Heads
- Expected Value vs Risk: Coin Flip Betting Games
- Expected Waiting Time in Poisson Process
- Expected Winnings in Dice Comparison Game
- Geometric Series and Quick Probability Calculations
- HHT vs HTT Pattern Race
- Identify Copper Coins Box with Single Weighing
- Kelly Fraction for an Even-Money Bet
- Largest Amount Unattainable with 5¢ and 11¢ Stamps
- Minimum Races for Top 3 of 20 Horses
- Monte Carlo Estimation of Pi
- Normal Approximation for Binomial: At Least 50 of 400 Pass
- Odd Heads with Mixed Fair and Biased Coins
- Optimal Question for Guessing Coin Sequence
- Phone Number Coincidence: Chance or Significant?
- Probability Black Balls Are Not Adjacent
- Probability of Even Heads with N Fair Coins
- Probability of Game 7 in Best-of-Seven Series
- Probability of Meeting at Train Station
- Probability of More Than 550 Heads in 1000 Coin Flips
- Probability of Strictly Increasing Die Sequence
- Probability Product of Two Dice is a Perfect Square
- Red-Black Card Game with Optional Stopping
- Secure Average Salary Computation
- Strategic Dice Betting with Information Asymmetry
- Tennis Game Win Probability from 30-30 with 70% Point Advantage
- Tennis Win Probability from Deuce with 60% Point Win Rate
- Three Random Dots on Square Edges
- Weekend Pizza Probability
- Weekend Rain Probability (Independent Events)
- World Series: Probability of Going to 7 Games
- Ball Color Guessing Game: Expected Winnings
- Colored Runs of Cards
- Dice Ratio Game: Choose Best Payout
- Distance from North Pole
- Expected Count of Uniform Variables Until Sum Exceeds One
- Expected Distinct Values in Sampling with Replacement
- Expected Rolls for Two Consecutive Sixes
- Expected Uniform Samples Until Sum Exceeds One
- Frog Cover Time on 4 Circular Lily Pads
- Minimum Races to Find Top 3 of 25 Horses
- Optimal Door Selection: Three Coin Tosses
- Padel Game Win Probability at 9-9 Against Stronger Opponent
- Random Point on Disk
- Random Walk on Cube: Expected Steps to Opposite Corner
- Random Walk: Reaching Target Before Barrier
- Sports Betting Arbitrage with Plus Odds
- Sum of Uniforms Exceeding One: Expected Count
- Upper Bound on Third Correlation Given Two Others
- Valid Range of Equal Pairwise Correlations for N Variables
- Variance of X-Coordinate for Uniform Points on Unit Circle
- Weekend Rain Probability Bounds (No Independence Assumption)
- Airplane Boarding: Last Passenger's Seat