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 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.
Bag has 5 pennies, 10 nickels, 4 dimes. Draw without replacement. P(nickel then dime)?
Use inclusion-exclusion principle to find P(female OR math major). Solve this probability union problem with a Venn diagram.
Find probability both pens are non-defective when selecting 2 from 12 (3 defective). Use combinations.
Basket has 4 apples, 5 oranges, 2 bananas. Jonas picks one, Beth picks next. P(orange then apple)?
Find P(red car OR speeding ticket) using a two-way frequency table. Learn inclusion-exclusion and conditional probability.