Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
The first problems apply single rules. Later ones combine tables, trees and real situations such as quality control and medical testing.
Standards: S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7 · Level: Grade 11 Algebra 2
Problem 1 Sample space for two stages ★★★
A coin is flipped and a six-sided die is rolled. List how many outcomes are in the sample space and find P(heads and an even number).
Problem 2 Complement of an event ★★★
A shuttle bus arrives on time with probability 0.88. Find the probability that it does not arrive on time.
Problem 3 Events as subsets ★★★
Let the sample space be {1, 2, …, 12}, A = multiples of 3 and B = even numbers. List A ∩ B and find P(A ∪ B).
Problem 4 Addition rule ★★★
Suppose P(A) = 0.62, P(B) = 0.41 and P(A ∩ B) = 0.27. Evaluate P(A ∪ B).
Problem 5 Mutually exclusive events ★★★
In one visit to the library, Noor borrows a novel with probability 0.2 or a biography with probability 0.5, but never both on the same visit. Find the probability she borrows at least one of the two types and the probability she borrows neither.
Problem 6 Check independence ★★★
At a raffle, 35% of tickets are blue, 20% of tickets are marked with a star, and 7% are both blue and starred. Are “blue” and “starred” independent events?
Problem 7 Two free throws ★★★
A player makes 70% of free throws, and shots are independent. Find the probability of making both of two shots and of making exactly one.
Problem 8 Venn diagram of language classes ★★★
Among 35 students, 19 take Spanish, 13 take French and 7 take both. The Venn diagram shows the counts in the three inner regions. Find the number taking neither language and P(French | Spanish).
Problem 9 Two-way table probabilities ★★★
The table shows phone type by grade for 120 students. Find P(iPhone), P(Junior | iPhone) and P(iPhone | Senior).
Problem 10 Conditional probability formula ★★★
In a survey, 35% of teens own a skateboard and 14% own both a skateboard and a helmet. Find the probability that a teen owns a helmet given that the teen owns a skateboard.
Problem 11 Draws without replacement ★★★
A jar holds 7 mints and 5 toffees. Maya takes two candies, one after the other, without putting any back. Find the probability that both are mints.
Problem 12 Test for independence in a table ★★★
Use the table of 120 students from the earlier problem. Are the events “Android” and “Junior” independent? Justify with probabilities.
Problem 13 Conditional from percentages ★★★
In a neighborhood, 60% of households own a pet and 25% own both a pet and a bicycle. Find the probability that a household owns a bicycle given that it owns a pet.
Problem 14 Addition rule with a table ★★★
Using the same table, find P(Junior or Android).
Problem 15 Union with cards ★★★
One card is picked at random from a full deck of 52. Find P(face card or spade), where the face cards are jack, queen and king.
Problem 16 Two alarms ★★★
Two independent alarm clocks each ring with probability 0.92. Find the probability that at least one rings.
Problem 17 Defective parts from three factories ★★★
Plant A makes 40% of a company’s chargers with a 1% defect rate, plant B makes 35% with a 4% defect rate, and plant C makes 25% with a 2% defect rate. Find P(defective) and P(made by B | defective) to the nearest thousandth.
Problem 18 Two dice, conditional ★★★
Two fair dice are rolled and the sum is 8. Find the probability that at least one die shows a 6, given that the sum is 8.
Problem 19 Allergy screening ★★★
A rare allergy affects 3% of campers. A screening patch shows a reaction for 90% of campers who have the allergy and for 5% of campers who do not. A camper shows a reaction. Find the probability that the camper has the allergy, to the nearest hundredth.
Problem 20 Independence of a complement ★★★
Show that if A and B are independent, then A and B′ are also independent.
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