Probability Word Problems
Probability problems ask you to figure out the chances of something happening — drawing a red marble from a bag, rolling a certain sum with two dice, or selecting a committee with specific characteristics. What makes these tricky isn't usually the math itself (which often comes down to counting and dividing) but correctly identifying what you're counting. You need to distinguish between "and" (multiply) and "or" (add), between "with replacement" and "without replacement," and between situations where order matters (permutations) and where it doesn't (combinations). Getting these distinctions wrong is easy and gives you an answer that feels right but isn't, which is exactly why these problems are so valuable for building mathematical reasoning.Find the probability that a 3-digit security code (digits 0-9, no repeats) contains exactly 8, 3, and 1 in any order.
Find minimum games needed for >99% chance of at least one win with 57% individual win probability.
Find probability luggage arrives using conditional probability. Two paths: on-time flight (0.8) vs delayed (0.6).
P(smoker) = 11%, P(cancer|smoker) = 0.34, P(cancer|non-smoker) = 0.03. Find P(smoker|cancer) and test independence.
Find probability no current employee interviewed until 2+ noncurrent employees interviewed. Combinatorial problem.
Find the probability a jury of 12 is all women from a pool of 24 men and 25 women.
Bag has 5 pennies, 10 nickels, 4 dimes. Draw without replacement. P(nickel then dime)?
Two-way frequency table: 122 students. Find P(female OR left-handed) using probability addition rule.
Find the probability of selecting one apple and one orange from two different baskets. Multiple methods.
Two balls drawn without replacement from box with red, white, black balls. Find P(same color).